M Koehl

G Piasny

V Thomine

P-A Garambois
email: pierre-andre.garambois@irstea.fr

P Finaud-Guyot
email: pascal.finaud-guyot@umontpellier.fr

S Guillemin
email: samuel.guillemin@insa-strasbourg.fr

L Schmitt

4D GIS FOR MONITORING RIVER BANK EROSION AT MEANDER BEND SCALE: CASE OF MOSELLE RIVER

Keywords: Morphodynamic monitoring, diachronic analysis, geodetic surveying, photogrammetry, UAV, 4D GIS

The "Wild Moselle" regional nature reserve extends over 13 km at the western foothills of the Vosges Mountains (France). The hydrological regime of the river is characterized by high flow in winter and spring and low flow in summer. Its average slope is 0.12 % and its average bankfull width is 60 m. The coarse sediment load comes mainly from bank erosion. Although this sector is relatively less affected by past or present human activities, the propagation of morphodynamic adjustments initiated by actions carried out both upstream and downstream of this sector impacts the current functioning of the river. These erosion waves converge today towards the central part of the reserve, which led to the collapse of the central pier of the Bainville-aux-Miroirs bridge during a 2-year flood in 2011, and could induce potential risks of defluviation which may destabilize infrastructures. In this context, the study carried out aims to characterize and anticipate the morphodynamic evolutions of the Moselle to be able to propose scenarios of management and restoration of the lateral mobility of the river. For this purpose, a 2D hydro-sedimentary model is being built over the entire reserve, combined with a detailed morpho-sedimentary monitoring. In order to improve the understanding of the lateral migration of the Moselle River, a photogrammetric monitoring was carried out along the concave bank of the most active meander of the studied sector. To follow this morphological evolution more closely, it was decided to establish a 4D GIS. The objective of this monitoring is to compare the rate of bank retreat with hydrodynamic parameters in order to estimate the geotechnical properties of the bank. Comparison of the observed and modelled bank retreat must thus allow these different parameters to be calibrated in the hydro-sedimentary model. As part of this work, this paper aims to highlight the use of 4D GIS to monitor bank retreat at the scale of a meander bend and is divided into three different parts: (i) a state of art to situate the study into the current knowledge and technologies, (ii) a presentation of the study area and the measurements carried out and (iii) a description of the different 3D or 4D data produced and the consequent spatial analyses.

INTRODUCTION

Data management and representation have made great progress last decades notably in moving from 2D to 3D and integrating time. This type of representation has developed considerably in the world of geo-information, mainly because of the evolution of processing and visualization algorithms but also thanks to the multiplication of survey techniques. As a result, it becomes easier and easier to model a portion or even a territory in 3D. Two technologies play a major role in these developments: laserscanning and photogrammetry. [START_REF] Pfeifer | Overview of TLS systems, overall processing and applications[END_REF] defines terrestrial laser scanning as a data acquisition technique using laser light to directly measure, in a regular frame, the coordinates of 3D points on surfaces at an Earth position. A 3D terrestrial laser scanner (TLS) is a device that uses this process to determine X, Y and Z points coordinates in order to acquire a point cloud of the area. Laser-scanning of an area using a laser scanner, whether terrestrial or aerial, provides 3D point clouds of the entire area with a configurable point density depending on the equipment and the recording conditions. The other technique implemented to obtain 3D models, is based on photogrammetry from images that can also be aerial, from UAV, or terrestrial. Aerial photography has long been used for * Corresponding author mapping applications. Many applications result from it. One of its main advantages is the minimization of field work. Photogrammetry has now become a widely used technique even for local scale mapping applications. This technique allows the user to obtain 3D data from an area of interest. It is also used to produce orthophotos. Photogrammetry has also experienced a new boom with the development of the use of UAVs (unmanned aerial vehicles) for mapping, particularly on a larger scale. Photogrammetry by UAV is particularly interesting in sites requiring rapid intervention, including the case of inspection and monitoring [START_REF] Murtiyoso | Acquisition and processing protocols for UAV images: 3D modeling of historical buildings using photogrammetry[END_REF] [START_REF] Jaud | DRELIO : Un drone hélicoptère pour le suivi des zones littorales[END_REF]. It is therefore possible, from images with well-defined overlapping areas, to determine the relief and contours of an object or territory in the form of point clouds obtained from dense matching techniques. Digital Terrain Models (DTM) and Digital Surface Models (DSM) are used as digital representations of the natural terrain. Such acquisitions can be made several times under the same conditions and with sufficient precision to be compared. The multi-temporal data also allow to display local changes in topography. Indeed, by comparison with a reference model, topographic and/or height changes can be quantified and represented. This was used to evaluate the accuracy of digital surface model (DSM) of river-channel morphology derived from the imagery acquired with a low-cost digital camera on board an unmanned multi-copter [START_REF] Watanabe | UAV photogrammetry for monitoring changes in river topography and vegetation[END_REF]. Crosssections make it possible to highlight in a very explicit way these topographical evolutions. The DTM/DSM generated directly from the point cloud is an ideal support to analyze morphological evolutions in some cases and estimate sediment budgets [START_REF] Eschbach | Combining geodetic and geomorphic methods to monitor restored side channels: feedback from the Upper Rhine[END_REF][START_REF] Rivas Casado | Towards a Transferable UAV-Based Framework for River Hydromorphological Characterization[END_REF]. By combining the DTM and aerial photographs, it is also possible to produce georeferenced orthophotos that can be integrated into the 4D GIS and serve as additional support for analysis, especially on smaller scales [START_REF] Dawod | Projected impacts of land use and road network changes on increasing flood hazards using a 4D GIS: A case study in Makkah metropolitan area, Saudi Arabia[END_REF]. The advantages that UAVs can provide for the survey of small areas, as meander bends, are however very interesting. UAVs are alternatives to quickly recording data (images) to compute a 3D model of a small area. In fact, UAVs show the advantage of being inexpensive, whether in financial or human terms, and their size and weight make them easy to deploy and implement. Considering these advantages, a photogrammetric monitoring using UAV was carried out along the concave bank of the most active meander of the Moselle River in order to better understand and model the lateral migration of the river. In order to survey this fluvial morphodynamic process more closely, a 4D GIS has been established along the meander bend. The objective of this monitoring is to assess the bank erosion rates according to hydrodynamic parameters (discharges, water levels, flow velocities, shear stresses, etc.) and geotechnical properties of the eroded bank (rest angle, bank sediment stratigraphy, vegetation, etc.). Subsequently, comparison of observed vs modelled bank retreat should allow calibrating the geotechnical parameters into a 2D hydro-sedimentary model. This paper is divided into three parts which: (i) describe steps from photogrammetric monitoring to point of clouds construction, (ii) present a method to extract bank profiles and (iii) show how to integrate photogrammetric data into a GIS also including other topo-bathymetric data.

STUDY SITE

The Moselle River drains a catchment area of 1976 km² from its source at Bussang in the Vosges Mountains to Tonnoy at the Lorraine plateau. The "Wild Moselle" regional nature reserve extends over 13 km at the western foothills of this massif. The river's hydrological regime is characterized by high flow in winter and spring and rather low flow in summer. Its average slope is 0.12 % and its average bankfull width is 60 m. The load originates quasi-exclusively from bank erosion. Although this sector is relatively less affected by local past or present human activities (bank stabilization, river bed gravel extraction, floodplain gravel mining, etc.), the propagation of morphodynamic adjustments initiated by actions carried out both upstream and downstream this sector impact the current functioning of the river: regressive and progressive erosions that can foster strong lateral erosion, meander cutoff, channel contraction, etc. So the waves of both regressive and progressive erosion converge today towards the central part of the reserve, which led to the collapse of the central pier of the Bainville-aux-Miroirs' bridge during a 2-year flood in 2011. These dynamics could also induce a potential risk of avulsion which may destabilize other infrastructures along the studied river reach. In this context, the underway study aims to characterize and anticipate morphological evolutions of the Moselle River to be able to propose scenarios of management and restoration of the lateral mobility of the river. To reach this purpose, a 2D hydrosedimentary model is being built over the entire natural reserve, which is combined with a detailed morpho-sedimentary monitoring. This consists in topo-bathymetric LiDAR data, hydrological surveys (limnimeters, ADCP -Acoustic Doppler Current Profilers), and morpho-sedimentary surveys (sediment tracking -2500 pit-tags, grain size measurements on both surface and subsurface).

BANK SURVEY

From UAV photogrammetric data acquisition to point clouds

To highlight the evolutions of the banks of the Moselle, it is necessary to be able to compare topographical data at different dates. In order to obtain results showing significant changes, it was decided to acquire data after each morphogenic flood, when the water level was low enough to characterize the complete bank profile, from the bank top to the bank toe. As shown in Figure 4, several floods occurred during 2018-19. For accessibility, timing and organization reasons, four dates were chosen for the recording of in situ data. As previously defined, it was decided to test the acquisition of photogrammetric data using a DJI Phantom 3 UAV. The covered area consisted in the concave bank for a length of about 700 m. Following the classic considerations [START_REF] Remondino | UAV photogrammetry for mapping and 3D modeling -Current status and future perspectives[END_REF], a typical image-based surveying with UAV systems requires a mission planning, GCPs measurement for geo-referencing, image recording, camera calibration, and image orientation, image processing for 3D modeling and information extraction. The first date was an experimental operation to define the first state of the meander and to calibrate the field operations. More than 1,000 images (Table 1) were recorded during each mission, whether in nadiral or oblique views (Figure 2). On some of them, coded circular targets are visible. These were used to materialize GCPs (Figure 3): the GCP coordinates were then measured with a geodetic GNSS receiver. The measured and automatically extracted points using Agisoft Metashape software are in the centre of the targets and their coordinates have been determined in the French RGF93-CC49 system.

The flight plan was executed manually. As authorized in France for visual drone flights, it consisted of several 300 m long areas. Each areas was recorded in multiple passages with nadiral views and several passages with oblique views at 30° and 60°, perpendicular to the bank or inclined by 30°. The overlapping of the successive photos is about 60%. The flight time of about twenty minutes made it possible to make these shots without problems. The shooting trigger was set to automatic shooting at 2 s. The height of the flight was between 20 and 40 meters which allowed to obtain a pixel size of 1 cm.

Limnimeters have also been located upstream and downstream of the meander in order to records water heights during the studied periods.

Generation of point clouds.

Large quantities of images were therefore acquired by drone for each measurement campaign. Among this mass of data for each campaign, a sorting was carried out, to preserve only images with a good quality. Two selection methods were applied: (i) a qualitative selection apparent to a visual analysis of the images to eliminate the unusable images (duplicates, under or overexposed images). In this first method, the operator's analysis is heavily used to make a manual selection; (ii) a quantitative selection using the Metashape software to estimate the quality of an image, by means of a coefficient. A blurry image, therefore unusable, will have a coefficient of 0.50. To maintain only good quality images, the acceptability threshold for this coefficient has been set at 0.75. Table 1 shows the number of images acquired and the number finally used in processing, corresponding to a ratio from about 50 to 80%. In the end, the selection was a little harsher for the first and third acquisition campaign because of the weather conditions (very hot sunshine). Nevertheless, the number of photos used was sufficient to meet the overlay criteria.

Table 1: Images used

The UAV used to take pictures of the meander was a DJI Phantom 3 pro multi-copter. This device has the advantage of being light and easy to handle. It has its own positioning system (GNSS) which gives the position of the drone at each image recording with a quasi-metric accuracy. However, this relative inaccuracy has been a disadvantage in the calculation of precise camera locations since the software relies on these initial values.

Consequently, the coordinates available in the metadata (Exif) of the images were not used.

Figure 3: Bank morphology and coded targets as GCPs

Identification and visualization of GCPs in a GIS.

As the length of the studied meander is quite substantial, the number of available coded targets for georeferencing was too low. These were therefore reused several times using the same cut-out as allowed by the maximum flight distances. The targets were renamed and matched thanks to their location in a GIS layer (Figure 4).

Figure 4: GCPs in GIS layer

The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIV-4/W1-2020, 2020 3rd BIM/GIS Integration Workshop and 15th 3D GeoInfo Conference, 7-11 September 2020, London, UK

Creation of the point clouds

For organizational reasons, each model was divided into chunks, treated separately, and then merged into a single point cloud per campaign. The different processing steps followed a classic photogrammetric process: (i) relative orientation of the images -Align Photos -to move from image coordinates to model coordinates from which a sparse point cloud can be generated. This was done through the automatic extraction of key points in each image which are then paired with the key points of neighboring images to generate tie points. Sfm (Structure from motion) algorithms then allowed the calculation of the relative orientation of the images from which was deduced a 3D point cloud; (ii) georeferencing of the point cloud thanks to the GCPs imported and detected automatically (markers) thanks to the coded targets -Optimize Camera -. The accuracy of the different obtained 3D models was about 2-3 cm; (iii) another adjustment was undertaken, but this time to check the criterion of accuracy. Some GCPs were transformed into check points. Errors on check points were always greater than errors on GCPs which denotes an existence of a systematism that could be explained by a pixel size larger than the precision of the coordinates. However, we get an accurate model. The next step is the generation of the dense point cloud -Build Dense Cloud -. At this level, the software increases the amount of points by densifying the cloud from the images. Densification quality parameters can be set at this stage.

The number of points in high quality is, for example, four times higher than that obtained by placing the parameter at Medium (for example, for a band of 700 m long over a depth of 30 m, 4.4 million and 1.1 million of points, respectively). Last step was to clean out the unnecessary noises and points and reduce the model to a 10 m strip around the bank. After this stage, 4 georeferenced 3D point clouds, denoised and cleaned were available for analysis and interpretation (Figure 5). The format is widely used and regarded as an industry standard for LiDAR data. From our field observations, we expected significant deviations (in the order of several meters). Despite CloudCompare is an adequate tool to distinguish changes between two nearby point clouds (for example, for auscultation), but was not efficient in our case. We therefore used the overlay of georeferenced point clouds to quantify the bank erosion.

It was then necessary to analyze the bank evolutions with another medium to have more information about it. The realization of cross-sections is an interesting option, but only with a 2D view (in this case x and z). Metashape does not offer tools to directly calculate profiles. For this reason the data were exported and superimposed in 3DReshaper software package. The realization of cross-sections required the definition of an axis according to which these were to be calculated. For such needs, all point clouds have to rasterized in CloudCompare with a grid size of 1 m, when local slopes were calculated using ArcGIS package.

Based on slope discontinuity, a line was drawn along the river banktop for each campaign, from the limnimeter to the downstream opposite side. Considering that profiles were built perpendicularly to the banktop line, this line was smoothed using Bezier curves tools, in order to estimate as far as possible vertical profiles. The reference line chosen to build profiles was the banktop line of the first acquisition. Vertical profiles were automatically extracted each 10 m using 3DReshaper software with a section thickness of 0.1 m and a maximal edge distance of 0.5 m. Profiles were extracted from 0 to 540 m which corresponds to the overlapping area between all surveys. The profiles length of 15 m is constant and corresponds to the observed maximal bank retreat. Extracted profiles were manually cleaned in Autodesk in order to remove points corresponding to vegetation and smooth the bank profiles. Each cleaned 2D lines was saved as DXF AutoCAD file and a Matlab program was developed in order to automatically open these files and superimpose them (figure 6).

The stratigraphical limit between the fine and coarse sediment layers was visually defined using point cloud textured 3D model of the first survey, because the image brightness allowed to identify both layers. The elevation of this limit was supposed to be constant during the surveying period. Submerged data was however not exploitable in the sense that it was highly noisy, due to the reflection of water and the change of medium. Therefore, to be consistent, each profile was cut off at the elevation corresponding to the highest water level being observed during all of the surveys. In fact, water levels of the first and last surveys were relatively low and similar, but the water level of the third survey was 60 to 70 cm higher. Thus, the water level measured during this campaign was used as lowest reference. This shows the importance to collect data during low flow in order to dispose of the most complete bank profile. But, as indicated in figure 7, available survey windows were restricted over the year and especially during the spring and the winter.

DIACHRONIC PROFILE ANALYZES

Areas under each bank profile (figure 6) were calculated in Matlab and the eroded surfaces were deduced by subtracting values obtained between each survey. As the bank height varied along the meander bend, each bank profile was normalized, in order to be able to compare the surface eroded between profiles extracted at different locations. Therefore, for each profile, the banktop elevation was considered as 1 m, while the bank toe elevation was considered as 0 m. Thus, if between two surveys, the bank retreated of 1 m and the shape of the both bank profiles was constant, the calculated eroded surface equals 1 m². For each profile, eroded areas were cumulated and represented in figure 8.

There are no values at 400 m because of the presence of a tree, which felled into the channel during the study. Finally, in order to compare the observed eroded areas to the observed retreats of the banktop, a Matlab program was developed to automatically identify banktop positions along the profiles. Banktop retreats of the first studied flood were not represented because the banktop positions were nearly identical. the bank profile is due to the presence of a paleochannel that was filled by fine sediments over the time. Another paleochannel was also visible at 270 m, 350 m and 410 m, but with a reduced width (5-10 m) and depth (0.6-0.8 m). However, the erodibility of the fine sediment layer is lower than this of the gravel layer, due to cohesion forces. Thus, the presence of former channels into the concave bank controls the bank retreat rate, and more generally the current morphodynamics of the meander (Eschbach et al., under review). Furthermore, bank retreat discontinuities observed at 150 m and 400 m are also due to the presence of a road that was eroded during 2011 and which currently continues to be eroded (figure 5). Along this road some trees are now located close to the banktop and their roots now enhance the bank stability. However, at 400 m, it is no longer the case as shown by the comparison between the third and the fourth surveys. During the two last survey periods, observed bank erosions were concentrated in the center part of the meander bend, but were slightly higher in the downstream part of the meander bend. Maximal bank retreat was in average 14 m which results in a total bank erosion of 14 m during the last survey period. Globally, banks were stable at the beginning and the end of the meander bend due to low hydraulic conditions and also because they were stabilized by vegetation, blocks and/or fine sediments.

INTEGRATION OF PHOTOGRAMETRIC DATA INTO GIS AND COUPLING WITH BATHYMETRIC DATA

The point cloud extracted from the last photogrammetric campaign was combined with a bathymetric survey in order to study the development of the meander bend. Bathymetric data were collected using an acoustic Doppler current profiler (ADCP) coupled with an accurate differential GPS (DGPS). Recorded water depths were associated to DGPS coordinates during the post-processing via timecode according to a time step of 1 second. Field measurements were carried out after the photogrammetric campaign at higher water levels to have an overlay between both datasets and facilitate point clouds merging. The boat trajectory followed a zigzag path from one side to the other side of the river to optimized the river bed mapping and simplify interpolation between each transects. Some longitudinal profiles were also carried over the thalweg and along both river banks to complete this dataset and characterize the maximum lateral extension of the river bend. However, longitudinal extension of the bathymetric survey was reduced to the central part of the meander compared to photogrammetric surveys due to riffles located at each bend inflection which prevents taking measurements from a boat. Moreover, as the water levels were low during the survey, acoustic beams were concentrated in a small area and lateral beams did not improve the river bed mapping. Therefore, only the vertical beam was used to map the meander bend bottom. These bathymetry points were interpolated using a Triangular irregular networks (TIN) available in ArcGIS software. Edges of the TIN were manually adjusted in order to connect nodes between transects according to flow paths. Some bathymetry outlier points were delete as well during the TIN construction. Meanwhile, image-based point clouds was rasterized in CloudCompare, with a grid size of 1 m, to be consistent with the LiDAR resolution. This raster was converted to points and points were added to the previous TIN. During these steps, data resolution was altered by averaging elevation of points contained in cells, but this process is considered as negligible at the scale of our study. Results may however be affected by this approach in case of over-hanging riverbanks, in this instance cantilevered bank profile are replaced by a vertical wall throughout rasterization. As shown in this study, the cantilever is not the main bank failure mechanisms along the meander bend, which justifies the method we used. Likewise, this data are integrated in a 2D mesh and modelling results will be compared to a topobathymetric LiDAR. So, the bank retreat of the basal layer will not be investigated here. Furthermore, before merging photogrammetric and bathymetric point clouds, underwater points were deleted from the imagebased dataset. Indeed, elevation accuracy of underwater points was difficult to estimate without underwater ground control points at the time of the survey. However, the influence of refraction on underwater three-dimensional reconstruction may be estimated, but this may also be affected by the water turbidity.

Considering that turbidity varied from one campaign to the other, integration of underwater points did not seem relevant as a quick and easy way to study bank retreat. In fact, most surveys were carried out with a water level below the bank toe. So, all the bank profiles were characterized satisfactorily. At the end of the data processing, the TIN model including concave bank and river bed was converted to a raster with a grid size of 1 m.

Comparison between bathymetric surveys and LiDAR topobathymetric acquisition shows an average offset of 9 cm of the river bed elevation all over the reserve. Although absolute elevation of photogrammetric and bathymetric data is supposed to be more reliable than LiDAR data, it was more convenient to shift the elevation of the raster over the meander bend than the whole river reach. Indeed, as part of this study, monitoring of morphological evolution of the river bend allows to use relative elevations.

Finally, both meander and LiDAR raster were superimposed and mosaicked together in order to constitute the pre-flood topography. This approach was possible because the LiDAR acquisition followed the studied flood, without that other morphogenic events occurred. In fact, we could also use the LiDAR from the past year to build the pre-flood state, but occurrence of several floods before studied period made us consider that post-flood LiDAR was more representative of the initial topography of the river. However, post-flood LiDAR acquisition took place at the end of the summer, mass failures could also have occurred due to river dewatering, which may have modified bank profiles without floods. Thus, eroded areas could be overestimated by this comparison, but at the scale of the observed bank retreat this potential amount of sediment is considered to be negligible. Comparison of pre and post-flood states is presented in figure 9, the TIN model based on bathymetric and photogrammetry cloud of points overlay LiDAR Digital Elevation Model (DEM). Four cross-sections were extracted from both DEM and superposed in order to show the morphological evolution of the river bend:

-first cross-section shows that pre-flood profile is well fitted to post-flood profile at the upstream part of the meander. This shows that no lateral erosion occurred during the studied period on this area; -this was also the case at the end of the river bend, downstream the last cross-section. This confirms that TIN elevation is well adjusted to the LiDAR DEM and validates the accuracy of data acquisition and of the TIN construction process; -intermediate cross-sections also show a good fit between field measurements and LiDAR acquisition when comparing floodplain elevations. The fact that not morphological evolutions are observed between pre and post-flood states at the TIN extremities ensures that field surveys extends enough upstream and downstream of the studied area. As presented in figure 9, maximal bank retreat was observed in the bend apex where approximately 4 m of bank material was eroded. Bathymetric survey contributes to study the morphological evolution of the river bed throughout meander lateral migration. Regardless to the cross-section position, results show that river depths remain relatively unchanged with the development of the meander bend. The deepest and shallowest sectors were respectively located at the upstream and downstream extremities of the studied sector, which is in accordance with a pool-riffle fluvial forms. In fact, riffle areas are generally located at bend inflections and spatial distribution of this geomorphological units remains relatively constant over time. Although, meander shifting dynamics does not appear to modify cross-sections shape, sediment deposition rates at the convex bank seems to be longitudinally distributed. Indeed, the amount of sediment deposited at the middle and the tail of this bank (cross-sections T5 and T7) is significantly lower than at his head (cross-section T3). These dynamics are associated with the progradation of the point bar head to the downstream direction as the meander bend develops. As highlighted by a step of a few centimeters at the junction between pre and post-flood states (cross-section T3), the progradation of bar head leads to overestimate the bar head elevation at the pre-flood state. Indeed, without photogrammetric or bathymetric data, the initial topography of the emerged convex bank was characterized by data acquired during LiDAR surveys. This local topographic extrapolation could change flow patterns modelling which could influence sediment transport results. Therefore, we suggest to conduct at the same time photogrammetric monitoring over the concave and the convex banks in order to survey the morphological evolution of the entire meander bend. They are other elements that could impact results of hydro-morphological modelling such as log-jams or riparian vegetation (Eschbach, under review). Fortunately, prior to the beginning of this study, a ten-year flood removed all log-jams of the meander bend, so that hydraulic effects of log-jams became negligible.

CONCLUSION

This project located on a particularly active meander of the Moselle River is part of a larger project that extends over the "Wild Moselle" nature reserve. The accurate 3D information acquired over several periods allows to follow the evolution of the banks in a particularly accurate way. The implementation of the drone, coded targets and GPS allows the acquisition of data for the monitoring of the banks in only a few hours. Data processing needs the same time laps, and the process put in place as well as Matlab workflow now makes possible to generate profiles and calculate volumes of bank erosion automatically. It is thus that such a project makes it possible to meet specialists from different fields, including topography and cartography with those of fluvial geomorphology.

PERSPECTIVES

A great amount of data has been acquired in recent years to study the Moselle River. 3D treatments play a fundamental role in modelling the knowledge of hydro-morphological phenomena.

The temporal dimension is also of crucial importance, especially in a context of high river morphodynamics. All data will be useful to build, calibrate and validate a 2D hydraulic and morphosedimentary model, to propose scenarios of management and restoration of the lateral mobility of the Moselle River.

AKNOWLEDGEMENTS

This study has been funded by the Water Rhine-Meuse Agency, the Region Grand Est (France) and the INSA Strasbourg, engineering school (department for civil engineering and surveying).

The authors would like to thank Ordnance Survey GB (www.ordnancesurvey.co.uk) and 1Spatial (www.1spatial.com/) for sponsoring the publication of this paper.

  a. Catchment of the Moselle River upstream Tonnoy b. Valley bottom of the Moselle River from Châtel-sur-Moselle to Tonnoy c. "Wild Moselle" Regional naturel reserve and d. Studied meander bend

Figure 1 :

 1 Figure 1: Study site location.

Figure 2 :

 2 Figure 2: Nadiral (top) and oblique (down) images of the studied bank.

Figure 5 :

 5 Figure 5: Planimetric evolution of the meander bend during the studied period3.5 Profile extractionFrom these point clouds, it was possible to analyze the erosion of the banks over time, and in particular the impact of each flood.The best way to show the planimetric evolution was to directly compare the four point clouds. For this we used the CloudCompare software package, which is a tool allowing comparison of point clouds. This analysis is intended to identify areas of high and low bank retreat. The interoperability between Metashape and CloudCompare was achieved through the LAS or OBJ formats. LAS is a file format designed for the interchange

Figure 6 :

 6 Figure 6: Bank retreat observed at 220 m from 2020-03-26 to 2019-04-03

Figure 7 :

 7 Figure 7: Hygrogram recorded during the studied year

Figure 8 :

 8 Figure 8: Cumulative normalized eroded areas (diagrams) and corresponding banktop retreats (curves) Results show that concave bank of the meander bend was barely eroded between the first and the second surveys corresponding to an unique flood that occurred in March 2018. This means that bank erosion threshold lies close or above to a discharge of approximately 120 m 3 /s. Comparison between second and third surveys shows that bank erosion of the meander bend started at 30 m and ended at 500 m (fig. 9). Maximal bank retreats were observed between 240 m and 350 m with an average value of -8 m. On the whole, the plan view of the observed bank retreat is oval shaped, with discontinuities located around 150 m and 400 m. Between 120 m and 150 m, the thickness of the fine sediment layer reached 1 m to 1.5 m, while this value was about 0.4 m to 0.5 m along the whole meander. This stratigraphic variation of

Figure 9 :

 9 Figure 9: Extracted cross-sections of pre-flood TIN model and post-flood LiDAR DEM of the meander bend.

Figure 10 :

 10 Figure 10: Stitched panoramic image of the studied meander (2019-03)

  The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIV-4/W1-2020, 2020 3rd BIM/GIS Integration Workshop and 15th 3D GeoInfo Conference, 7-11 September 2020, London, UK

The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIV-4/W1-2020, 2020 3rd BIM/GIS Integration Workshop and 15th 3D GeoInfo Conference, 7-11 September 2020, London, UK This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLIV-4-W1-2020-63-2020 | © Authors 2020. CC BY 4.0 License.

This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLIV-4-W1-2020-63-2020 | © Authors 2020. CC BY 4.0 License.


Pierre Maillot

Olivier Corby

Catherine Faron

Fabien Gandon

Franck Michel

KartoGraphI: Drawing a Map of Linked Data

Introduction

In recent years, a large number of semantic Web knowledge bases (KB) have been developed and published on the Web. The reuse and joint exploitation of multiple KBs requires them to comply with a number of good practices. To help the user identify a set of relevant and usable KB that answers her need, we propose the KartoGraphI Web application1 that provides visualizations of certain characteristics of KBs. It relies on a (meta)dataset describing KBs available on the Web, automatically generated by the IndeGx framework by querying KBs with SPARQL.

This paper presents a demonstration of KartoGraphI together with an illustration of the main features of IndeGx. It is organized as follows: Section 2 presents the IndeGx framework and generated dataset. Section 3 presents the KartoGraphI Web application. Section 4 presents the proposed demonstration and concludes.

2 IndeGx: Description of Semantic Web KB IndeGx is a framework designed to index public KBs that are available online through a SPARQL endpoint. The indexing process uses SPARQL queries to either extract the available metadata from a KB or to generate as much metadata as the endpoint allows it. The RDF data generated by IndeGx is expressed using a combination of well-established description vocabularies such as SPARQL Service Description, VoID and DCAT. The generated metadata not only describes KBs but also conveys an estimation of certain quality criteria. These metadata can be used either by humans e.g. to select suitable sources, or agents to automate processes such as query optimization or rewriting.

IndeGx processes publicly available KBs whose endpoints are listed on the LOD Cloud, Wikidata, SPARQLES [START_REF] Vandenbussche | SPARQLES: Monitoring public SPARQL endpoints[END_REF], Yummy Data [START_REF] Yamamoto | YummyData: providing high-quality open life science data[END_REF] and Linked Wiki. At the time of writing, IndeGx has processed and indexed 553 KBs. The generation of a KB description depends on the capabilities of its endpoint. In particular, complex queries, such as those using counting and string-based operators on large quantities of triples or disjunctions, may fail due to the limits in time and resources of the endpoint.

IndeGx can be extended with new KB description features as long as they can be extracted with SPARQL queries. Those new features will be used in future indexations. The operations made by IndeGx to extract metadata are described in RDF in a GitHub repository using the EARL and the Manifest vocabularies. This structure makes it possible to add operations used in other similar approaches. IndeGx already uses the operations described in the approaches SPORTAL [START_REF] Hasnain | SPORTAL: Profiling the Content of Public SPARQL Endpoints[END_REF] and SPARQLES.

Asserted Dataset Descriptions. Provenance information concerns, among others, a dataset's authors, contributors, editors, license, source datasets, generation method, date of creation and modification. Those provenance metadata are important for transparency of and trust in the KB. They are generally asserted by the KB creators as part of a VoID description, but are difficult to discover when they are not given. IndeGx extracts the available provenance information of a KB by looking in its dataset for metadata descriptions made using VoID, DCAT or SPARQL-SD vocabularies. We separate the most basic provenance metadata into 4 categories: the authorship, the licensing, the time, and the source. The results show that less than 1% of KBs with a public SPARQL endpoint contain such metadata.

Endpoint Capabilities. The content of a KB is only as reachable as its endpoint is available. Approaches such as SPARQLES [START_REF] Vandenbussche | SPARQLES: Monitoring public SPARQL endpoints[END_REF] estimate the performance of SPARQL endpoints using SPARQL queries. IndeGx reuses SPARQLES queries and extends them to survey the implementation of the features of the SPARQL language by endpoints. Data Quality Measures. Several criteria have been identified as indicators of the quality of a KBs, such as those listed in [START_REF] Debattista | Evaluating the quality of the LOD cloud: An empirical investigation[END_REF][START_REF] Yamamoto | YummyData: providing high-quality open life science data[END_REF]. IndeGx evaluates KBs according to several of those quality criteria using SPARQL queries.

Traceability of the indexing process. IndeGx generates traceability metadata for every operation done on every dataset. The metadata contain information such as the start and end time of each operation, the query submitted and the error returned if it so happens. The generated traces support the study of the average performance of endpoints and of the responses of each endpoint to determine some of their characteristics.

KartoGraphI: Drawing a Map from Semantic Web KBs

KartoGraphI is a Web application visualizing the data generated by IndeGx. It draws various visualizations and statistics grouped along several view points described below.

Used/Shared Vocabularies. The (re)use of well-known vocabularies in a dataset facilitates its re-usability by others and is one of the core principles of Linked Data. IndeGx extracts the list of vocabularies from the namespaces of classes and properties a dataset uses.

KartoGraphI first generates a visualization of the endpoints linked to all the vocabularies, including the vocabularies used by no other KB (Figure 1). Secondly, a refined version of this visualization focuses on well-known vocabularies by showing only a subset of 3 487 namespaces extracted from Linked Open Vocabularies (LOV) and prefix.cc. A major advantage of this refined visualization is to filter out any unknown vocabulary that may result of a typographical error or the non-respect of naming conventions. However, it can also filter out new or very specialized vocabularies that are not listed on those sites.

KartoGraphI also offers a third visualization that connects the endpoints to the keywords associated to their well known vocabularies. This association of endpoints and keywords can be used to identify the domains a KB pertains to.

Dataset Population. VoID allows to give statistics about the triples and instances present in a dataset. Such metadata give an idea of the scale of a dataset and the most advanced statistics can be used to optimize queries. After trying to retrieve such information from the metadata given in a KB, IndeGx uses SPARQL queries to update the retrieved metadata and as much as possible extract all the possible statistics that can be expressed with VoID. They include statistics such as the number of triples using a certain property with an instance of a certain class as an object. Such statistics are extracted using CPU-and/or memory-intensive queries that only endpoints backed by large hardware resources can answer.

Endpoint Capabilities. The results displayed by KartoGraphI (Figure 2), show that two-thirds of the endpoints tested by IndeGx support at least 80% of all tested SPARQL features. The endpoints from the remaining third either returned errors or did not answer any SPARQL query. Data Quality Measures. The quality of the data of a KB can be measured according to different criteria. Among them, one of the structural quality measures depends on the respect of community best practices such as avoiding the usage of blank nodes and RDF data structures such as lists, sequences, and bags. It is to be noted that vocabularies such as OWL and SHACL use blank nodes and data structures to define vocabularies. Due to that, this measure may not be adapted as it is for datasets such as ontology repositories. This kind of criteria appears to be well complied with among the KBs processed. The proportion of resources that are not blank nodes in a dataset is close to 100%. The proportion of triples that are not part of the definition of RDF data structures is 76.2%. Other quality measures include the interlinking of a KB with others, through the use of shared vocabularies. They also include the readability of the KB by humans, based on the presence of labels and short readable URIs. The interlinking of KBs is generally good among the KBs processed, with on average 75% of the vocabularies used in a KB being listed on vocabulary portals. On the other side, the readability of KBs is not good in general according to our measures: an average 42% of the resources have no label, and an average 49% of them do not have short URIs.

Geolocation. The geolocation of endpoints is often overlooked as metadata of a KB. Using only SPARQL queries, IndeGx could only get endpoint timezones as an indicator of their location. To work around this lack, KartoGraphI uses external APIs to determine the location of endpoints from their URL. The resulting map, shown in Figure 3, illustrates that, although the Linked Data is an international effort, it is over-represented in Europe whereas there is an "empty diagonal" from South-West to North-East, containing no publicly available KBs. It is however possible that KBs hosted by countries in this zone be listed in resources currently not considered by IndeGx.

Proposed Demonstration

The demo will be as follow: Attendees will be guided through the different visualizations of the KartoGraphI Web application. A commentary of the notable features observed in the KBs descriptions created by IndeGx from publicly accessible endpoints Fig. 3. Geolocation of the endpoints in KartoGraphI: green items represent an endpoints' IP locations; orange items represent endpoints that gave a timezone not matching this location.

will be given, as shown in the video available at http://prod-dekalog.inria.fr/ SubmissionESWC2022.

KartoGraphI and IndeGx offer a systematic evaluation of sets of publicly available endpoints based on SPARQL. They show that among the KBs with an endpoint listed as publicly available, one third of them are not reachable. The remaining two thirds are usable thanks to their reuse of common vocabularies. By contrast, the readability of their content is not high on average, very few contain self-descriptions. Their resources are in majority not labeled to describe their content to humans.

In future works, KartoGraphI and IndeGx will extract and present new features present in KBs such as the language tag present. In the future, KartoGraphI will also offer a query editor using IndeGx metadata to guide federated query writing using IndeGx metadata.

Fig. 1 .

 1 Fig. 1. Graph of the endpoints listed on LOD Cloud website and their vocabularies. The vocabularies are extracted by IndeGx from the namespaces of classes and properties of the datasets.

Fig. 2 .

 2 Fig. 2. Bar chart of the distribution of the endpoints according to their coverage of SPARQL features.

KartoGraphI: http: // prod-dekalog. inria. fr/

Acknowledgments

This work is supported by the ANR DeKaloG project, ANR-19-CE23-0014, and the ANR D2KAB project, ANR-18-CE23-0017.


Nader Sadeghi
email: nader.sadeghi@univ-grenoble-alpes.fr

Romain Magnan

Françoise Massines

Pressure broadening of 772.376 and 772.421 nm argon lines and kinetics of argon metastable atoms

Keywords: Argon 772 nm lines, Pressure broadening, Pressure shift, Tunable diode laser absorption spectroscopy, Dielectric barrier discharges, Collision, Population transfer

Tunable diode laser absorption spectroscopy is used for recording the spectrally mixed profiles of argon 772.376 nm (2p7-1s5) and 772.421 nm (2p2-1s3) lines at different argon background pressures between 0.3 and 1 atmosphere. The absorbing atoms in the Ar*(1s5) and Ar*(1s3) metastable states are produced in a plane-to-plane dielectric barrier glow discharge operating at 20 kHz. The pressure broadening coefficient w and wavelength shift, s of the lines, deduced from the analysis of their variation versus pressure of recorded profiles, are w1=28.3±2.0 pm (14.2±1.0 GHz) and s1=11.5±0.8 pm (-5.8±0.4 GHz) for 772.376 nm line and w2=36.3±0.5 pm (18.2±0.3 GHz) and s2=12.8±0.7 pm (-6.4±0.4 GHz) for 772.4207 nm line, at 1 bar and 300 K. The progressive enhancement with argon pressure of the peak densities ratio [Ar*(1s3)]/[Ar*(1s5)], reaching 0.3 at 1 bar, reveals the importance of Arinduced collisions for the population transfer from resonant 1s2 to the metastable 1s3 state. Also, the time variation of Ar*(1s) densities indicates the presence of a weak excitation channel outside the discharge current pulse initiated by the breakdown. This channel results from the heating of electrons by the electric field seen by the gas in the DBD gap.

Introduction

In the last decades, atmospheric pressure non-equilibrium room temperature plasmas (APRTP) attracted high attention due to their particular physical properties. Thanks to the presence of high energy electrons, these plasmas can dissociate stable molecules to produce highly reactive radicals, or provide large density of atoms and molecules in highly excited electronic states, in an environment with heavy particles remained close to the room temperature. These properties have stimulated their application to "local" treatment of heatsensitive surfaces in medicine 1,2 , sterilization 3, 4, 5, , material processing 6 and in many other domains (see also review papers 7,8,9,10,11 and references therein). In most of APRTPs, helium or argon is used as main plasma-generating gas and their metastable atoms play an important role in plasma chemical processes. These atoms can be the main factor of the plasma sustainment through Penning and chemi-ionization of the trace or admixture molecules 12 . They also can highly influence the production rate of reactive radicals through eion recombination of so produced molecular ions 13,14 . When modeling APRTPs, the knowledge of the gas temperature, Tg is of prime importance because most of the reaction coefficients of species present are Tg dependent 13,14,15,16 . One way to determine the gas temperature would be from the rotational temperature of a molecule present in the plasma as impurity 17,18 , but this technique cannot be used in high purity rare-gases. Another technique, currently applied in low pressure rare gas plasmas, is the use of an appropriate tunable diode laser for deducing Tg from the Doppler width of the Gaussian profile of a spectral line whose lower level is a metastable state of the rare-gas 19,20,21 . But in APRTPs, collision of the excited -emitter or absorber-atom with ground-state atoms induces the spectral broadening of the line (pressure broadening), which evidences by the presence of a Lorentzian component in their line profile. When the upper or lower level of the considered atomic transition is optically connected to the ground state of the collision partner, the interaction is dominantly dipole-dipole type, leading to "resonance broadening" with Tg -1 gas temperature dependence 22 . Otherwise, it is dipole-induced-dipole interaction, leading to the "Van der Waals broadening", whose temperature dependence is Tg -0.7 22 . Therefore, the knowledge of the pressure broadening coefficient of the line would permit the determination of the gas temperature from its recorded profile 23 .

In 1960-1970s, motivated by the determination of the oscillator strength of resonance lines of rare-gas atoms, but also for testing the applicability of different collision broadening theories, several groups have measured the pressure broadening coefficients of different argon lines. The resonance Faraday effect on some argon lines absorbed by metastable atoms has been used in 24,25 , but most of the line profiles were obtained from the analysis of the profile of plasma induced emission, by scanning Fabry-Perot interferometer [START_REF] Hindmarshi | Proc.phys. Soc. A[END_REF][START_REF] Stacey | [END_REF]28 or with a spectrometer 29,30,31,32 . However, the necessary correction for the apparatus function of the experimentally recorded spectral profiles of the lines introduced large uncertainty on deduced broadening coefficients. Moreover, often in thermal plasmas the gas temperature was not homogeneous and well defined 29,28,32 , introducing extra uncertainty on measured coefficients. But after the event of the spectrally narrow band tunable diode lasers and their use in absorption spectroscopy (TDLAS) technique, the correction of the apparatus function width was no more needed and the pressure induced widths and shifts of many argon lines ending on the four lowest excited states of argon (two metastable Ar*(1s3) and Ar*(1s5) and two resonant Ar*(1s2) and Ar*(1s4) 33 ), which are always highly populated in argon plasmas, have been measured by several groups [START_REF] Tachibana | [END_REF]35,36,37,38,39,40 41 . However, none of the above cited publications provided the pressure broadening coefficients of the 772.38 nm (1s5-2p7) and 772.42 nm (1s3-2p2) lines, which are studied in this work.

In this work, the absorption profiles of the combined 772 nm lines are measured in low energy glow type dielectric barrier discharges (DBD) for Ar pressures between 0.3 and 1 atmosphere. From these measurements, the pressure broadening coefficients and wavelength shifts of the 772.376 and 772.4207 nm lines are deduced. Also, the variation of the [Ar*(1s3)]/[Ar*(1s5)] density ratio versus the Ar pressure is pointed out and the kinetics of Ar*(1s) atoms in the pulse DBD is explained.

Experimental setup

Metastable atoms in Ar*(1s3) and Ar*(1s5) states, the lower levels of the studied transitions, are produced by dielectric barrier discharge (DBD) in pre-mixed Ar + 200 ppm of NH3 Penning gas. The metallic electrodes of the plane-to-plane DBD are covered by 1 mmthick, 70 mm x 70 mm dielectric plates made of alumina, with 2 mm gap between them. The discharge zone is 50 x 10 x 2 mm 3 volume, defined by the dimensions of electrodes. The whole DBD cell is contained in an air-tighten chamber. Before each experiment, the chamber is pumped down to 10 µbar and, to reduce the amount of impurity resulting from eventual air leak and degassing from walls, it is then flushed with 3 standard liters per minute (SLM) of the gas mixture. A needle valve between the chamber and the pumping pipe permits to adjust the total pressure in the chamber, measured with a capacitance gauge, between 0.3 and 1 bar.

Considering the 5 x 0.2 cm 2 section of the gas flow, the 3 slm flow rate and µ=2.2 x10 -5 Kg.m -1 .s -1 dynamic viscosity of argon, Reynolds number is smaller than 300 for all considered pressures, resulting in a laminar gas flow between dielectric plates. The top electrode of the DBD is powered by a 20 kHz generator (Keysight 33500B Series) followed by an audio amplifier (Crest CC4000) and voltage transformer (Boige & Vignal), while the bottom electrode is grounded. Depending on the pressure fixed in the chamber, the amplitude of the applied high voltage (HV) is adjusted (up to 2000 V peak value) for obtaining stable and reproducible discharges, but at the lowest possible voltage to limit the electron density.

Current-voltage characteristics are obtained using a high-voltage probe (Tektronix P6015A 75 MHz) and a current probe (LILCO LTD 13W5000), whose signals are recorded and processed on an oscilloscope (Tektronix MSO56). Figure 1 shows three V-I curves, over one period of the HV, for three pressures. The discharge current is characteristic of a glow DBD, free of microdischarges 42 . As the discharge covers uniformly all the DBD volume between electrodes, the discharge current was deduced by subtracting the displacement current (recorded at the same voltage but in an empty chamber) from the total current and the voltage applied to the gas gap Vg, was calculated by accounting for the charges deposited on the surface of dielectrics from the previous discharge 43 . As seen from this figure, higher the pressure, larger the applied voltage amplitude is. But in all cases, the peak discharge current remains about 20 mA (40 A.m -2 current density). Deduced from the V-I curves, for all studied pressures the dissipated power in the gas remains below 0.1 mJ per discharge pulse. The calculated gas drift velocity at 1 atmosphere is 0.5 m/s, corresponding to a residence time inside the discharge volume of 20 ms. Thus, the deposited power on the gas during the residence time of the gas is <40 mJ. Most of this energy is transferred to dielectric electrodes; both by heat conduction and by ion accelerated within the sheaths (see Ref 44 for more detail). The gas temperature deduced from the Gaussian component of the Voigt profile fitting the absorption lines at 312 mbar (see section 3.) is about 310 K. This very small increase of the gas temperature by the plasma action was also confirmed by the spectral simulation of the plasma induced emission intensity of the nitrogen first positive 4-1 band, at 678 nm, from atmospheric pressure argon + 0.04% N2 DBD (see Figure 2). Fitting parameter for the temperature was 305 ±10 K. Thus, at all pressures, the width of the Gaussian component of the Voigt functions fitting the experimental line profiles (see section 3) was fixed to w_G (FWHM)= 0.774 GHz = 1.54 pm= 0.706 step, corresponding to a gas temperature of 310 K.

Recording absorption line profiles

The spectral profile of the combined 772 nm lines is recorded by tunable laser absorption spectroscopy (TDLAS) technique 35,21 As already pointed out, metastables atoms in the DBD are mainly produced during the current pulses, whose duration is about 1-2 µs. Considering the about 1 µs lifetime of Ar* metastable atoms at the studied pressure range (0.3-1 bar) [START_REF] Robert | NIST Atomic Spectra Database[END_REF] , their densities evolve along the 50 µs period of the high voltage. It is thus not possible to obtain the absorption profiles by the direct continuous scan of the laser frequency, as is usually done in non time-varying plasmas, by the current scan of the DL [START_REF] Cunge | [END_REF]47,48 . The method we use consists in recording the timevarying transmitted laser signal (TVTLS) at various fixed laser wavelengths and using these records for obtaining the absorption profiles at different times of the HV period. The signal Sn(nt) of PD3, when the laser is set at the wavelength n of step number n, corresponds to the sum of the transmitted laser light, In(nt) plus the plasma emission E(t).

Thus, the time-varying plasma transmitted laser intensity can be deduced as In(nt)=Sn(nt)-E(t). The transmitted laser intensity before the start of the discharge pulse I0n(n) at t<0, thus in the absence of metastable atoms, provides the absorption-free laser intensity for the step N° n. Note the slight variation of the laser intensity with the wavelength, which should be related to the temperature variation of the DL, which is scanned by changing its temperature. For each step, thus n value, the Beer-Lambert law relates the time-varying absorbance 𝒜n(nt)

to the absorbing atoms densities, N(t):

𝒜 n (λ n , t) = Ln ( I 0n (λ n ) I n (λ n ,t) ) = (𝑘 5 . N 5 (t). φ 5 (λ n ) + 𝑘 3 . N 3 (t). φ 3 (λ n )). L (1)
where the subscripts 5 and 3 refer to metastable atoms in Ar(1s5) and Ar(1s3) states, with their respective densities N5(t) and N3(t) at time t in the HV cycle, L=5 cm is the absorption length in the DBD and k(m 3 ) is the line dependent absorption coefficient, defined as 41,49 :

𝑘 = 𝑔 𝑢 𝑔 𝑙 .
. 𝜆 0 4 .

𝐴 𝑢𝑙 8𝜋𝑐 (2)
in which gu and gl refer to the statistical weights of the upper and lower levels of the transition at wavelength 0 with Einstein coefficient Aul. 5(n) and 3(n) in Eq.( 1) are normalized profiles of the 772.38 and 772.42 nm lines, defined as ∫ 𝜑(𝜆). 𝑑𝜆 = 1.

A matrix is built, with 𝒜n(nt) files forming its columns and the time in the HV period being its rows. Once transposed, the successive columns of the new matrix provide the absorption profiles at different times of the HV period. As an example, two reconstructed absorption profiles from absorbance measurements in the 455 mbar DBD plasma are presented in figure 5. Profile in 5A corresponds to the time of the peak absorbance in the positive half-period of the HV. This time is at about 1 µs after the start of the discharge current. And the profile in 5B is in the afterglow, about 2.75 µs later than for 5A. The about 0.7 µs delay of the peak metastable density relative to the peak of the plasma induced emission, which corresponds to the peak of the discharge current in the DBD, results from the about 1 µs lifetime of Ar* metastable atoms. This delay also exists for all other pressures and is clearly seen in Fig. (4) for the 312 mbar plasma.

The reconstructed absorption profile is fitted with the sum of two Voigt functions, V5() and V3() (dashed blue and red curves in Fig. 5, respectively). They represent the pressure broadened absorption profiles of 772.38 nm Ar(1s5-2p7) and 772.42 nm Ar(1s3-2p2) lines, respectively. Their amplitudes inform us about the density of metastable atoms at different times for the considered pressure. The pressure broadening coefficients of the lines and the gas temperature can be deduced from the Lorentzian and Gaussian widths of the Voigt profiles. At fixed pressures, two sets of absorption measurements have been acquired and the concordance between the parameters of the reconstructed profiles from them has been verified. We have also observe that at given pressure, the width of the fitting Voigt functions remained unchanged (within 5%) whatever the discharge pulse position (positive or negative half-period of the HV) or the time in the period for which the absorption profile was reconstructed. This indicates a non-varying gas temperature during the LF period.

Pressure broadening and shift coefficients of lines

Reconstructed absorption profiles of the combined 772.376 nm and 772.4207 nm lines for the five studied argon pressures in the DBD chamber between 312 and 1000 mbar are presented in figure 6. Given the less than 10 MHz spectral width of the laser and its better than 100 MHz stability, tested over an hour by recording the amplitude of the transmitted peak of the Fabry-Perot interferometer, the apparatus function can be considered as negligible. Thus, profiles shown in Fig. 6 are the exact absorption profiles of the lines at corresponding pressures. The red vertical lines indicate the non-shifted positions of these lines, obtained from the peak absorptions in the low-pressure argon discharge cell. For each pressure, the black solid curve represents the best fitting to the experimental absorption profile with the sum of two Voigt functions, which are presented as blue and red solid curves for 772.376 and 772.4207 nm lines, respectively. To obtain the lowest noise level on reconstructed line profiles, those shown in Fig. 6 have been obtained at the peak absorbance, reached at the maxima metastable atoms densities. Also, the path of the laser beam in the gap of the DBD has been selected for having the largest absorbance. For pressures less than 0.5 bar, the laser beam crossed the DBD in the middle of the gap between electrodes but it was slightly shifted toward one of the electrodes at higher pressures. However, due to the quenching of metastable atoms by 3-body collisions with two ground state Ar atoms [START_REF] Robert | NIST Atomic Spectra Database[END_REF]50 , the density of metastable atoms continuously decreases with increasing pressure. The enhancement of the line-widths with increasing pressure is clearly evidenced in Fig. 6. 772.376 nm and 772.4207 nm lines, which are almost separated at 312 mbar, become completely mixed at atmospheric pressure. The shift of their central wavelengths relative to their respective zero pressure positions also increases with argon pressure. In DBD plasmas, the electron density barely exceeds 10 18 m - 3 44 , for which the reported Stark width of the lines would be 0.0007 and 0.0008 pm, respectively 51 . The Stark broadening of the lines can thus be neglected and the Lorentzian components of the Voigt functions fitting their profiles represent their pressure broadened widths. Figure 7 shows for both lines the pressure dependence of the full width at half maximum (FWHM) and shift (s) of their Lorentzian components. As expected from the theory, which will be discussed later, the pressure dependence is linear and the solid lines, which are the best linear fit to the experimental data (in black for the 772.4207 nm and in red for the 772.376 nm lines), have been forced to start from the origin of the pressure and of the ordinates in each case. The full width at half maximum (w) and shift (s) of these lines, deduced from their respective slops are: w1=27.7±2 pm.bar -1 and s1=11.3±0.8

pm.bar -1 for 772.376 nm line and w2=35.5±0.5 pm.bar -1 and s2=12.5±0.7 pm.bar -1 for 772.421 nm line. Reported uncertainties correspond to 2 of the fit +1.3% uncertainty from the wavelength gap between steps. However, given the estimated gas temperature of 310 K and the T -0.7 dependence of both width and shift parameters (see section 4.1), the broadening and shift values at standard conditions of atmospheric pressure and 300 K would be w1=28.3±2 pm and s1=11.5±0.8 pm for 772.376 nm line and w2=36.3±0.5 pm and s2=12.8±0.7 pm. In section 6.1, these values will be compared to available experimental data and theory prediction.

Theoretical broadening coefficient of lines

None of the lower or upper levels of the studied lines are optically connected to the ground state. Therefore, the broadening comes from the Van der Waals interaction of excited atoms with surrounding argon atoms. The FWHM of the Van der Waals broadening, vdW is expressed as [START_REF]A Physicist's Desk Reference[END_REF] :

Δ𝜆 𝑣𝑑𝑊 [𝐴𝑟] ≅ 3.0 𝑥10 -15 . 𝜆 2 . (𝐶 6𝑢 -𝐶 6𝑙 ) 2 5 ⁄ . (𝑇 𝑔 /𝜇) 3 10 ⁄ (3)
where [Ar] is the argon density (in cm -3 ),  the wavelength and vdW are in nm, µ=20 is the reduced mass of collision partners in atomic unit and Tg is the gas temperature. C6u and C6l are Van der Waals coefficients of upper and lower levels of the transition, expressed as:

C6=9.8 x 10 -10 p R 2 , in which the polarizability of the ground state argon is 53 p =1.64 10 -24 cm 3 and R 2 (in unit of Bohr radius a0) is a parameter defined as 25 :

𝑅 𝑖 2 = ( 5 2
) . ( . 〈𝑣 3/5 〉 (5) in which a0 is the Bohr radius and <v 3/5 > is defined as:

〈𝑣 3/5 〉 = 4𝜋. [ 𝜇 2𝜋𝑅𝑇 𝑔 ] 3/2
. ∫ 𝑣 2.6 . 𝑒𝑥𝑝 (-

𝜇.𝑣 2 2𝑅𝑇 𝑔 ) ∞ 0 . 𝑑𝑣 = ( 4
where ν corresponds to the mean relative velocity and R = 8.314 J/(mol.K). Corrected for the (4/π) 1/5 .Γ(1.8)=0.9775 factor, this leads to relation (7), in which the factor 3.0 in equation ( 3

Using this equation, the theoretical van der Walls broadening coefficients of 772.38 and 772.42 nm lines become 29.4 and 35.2 pm, respectively. These values will be compared to experimental data in section 6.1.

Absolute densities of Ar*(1s5) and Ar*(1s3) metastables

Integrating the absorbance in equation ( 1) over leads to:

∫ 𝒜 n (λ n , t). 𝑑𝜆 ∞ 0 = (𝑘 5 . N 5 (t) + 𝑘 3 . N 3 (t)). L (8)
As shown in figures 3 and 6, and discussed in section 3, the absorbance curves can be fitted with two Voigt profiles V5() and V3(), whose integrals are linked to the densities of Ar*(1s5) and Ar*(1s3) atoms, respectively. Reporting in (2) the transition probabilities of the lines: A772.38=5.18 x10 6 s -1 and A772.42=1.17 More, a comparison of the time evolutions of the discharge current (Fig. 4) and Ar* densities (Fig. 8), indicates that the enhancement of the metastable atoms density starts before the discharge current pulse. In Fig. 8, we also note the presence of these phenomena on both densities of Ar*(1s5) atoms, which are recorded at the positive half-period of the high voltage and those of Ar*(1s3) atoms, which are recorded at the negative half-period of the HV. All these observations, suggest a small, but undeniable production of Ar* atoms outside the discharge current pulses. This production should thus be related to the heating of plasma electrons, before and after the discharge breakdowns, by the weak electric field present in the DBD gap. A detailed analysis of these observations will be presented in section 6.3 after the discussion on the line profiles and the relative density of the two metastable species.

Discussion

On 772.38 and 772.42 nm line profiles

To our knowledge, there are only few works in which the pressure broadening of 772 nm argon lines has been studied, or when these lines have been used for the plasma diagnostic. Penache et al, who had the appropriate diode laser to access these lines, reported in their publication on characterization of high pressure microdischarges [START_REF] Penache | [END_REF] : "The analysis of the transition at 772 nm could not be pursued, since the collision broadening parameters were not found in the literature.". In a pulsed low pressure argon helicon plasma, Clarenbach et al have deduced the time variation of Ar*(1s3) metastable atoms by using laser absorption spectroscopy on 772.42 nm line and have deduced the gas temperature from the spectral profile of the absorption line 57 . We are aware of only two works reporting on characterization of 772 nm line profiles at high pressure. Moussounda and Ranson 28 have only measured the shift of the peak intensity of the lines emitted from a surfatron produced thermal plasma, with estimated gas temperature of 2000 K. Their reported shift values, corrected for the Tg -0.7 gas temperature dependence, would correspond to 13.5±0.7 pm and 14.5±0.7 pm at 1 bar and 300 K for 772.38 and 772.42 nm lines, respectively. The about 10% larger values of these authors, compared to ours, can probably be linked to an underestimation of the gas temperature in their spatially inhomogeneous thermal plasma. Williamson et al measured the density of Ar*(1s3) metastable atoms in a DBD plasma by laser absorption spectroscopy on 772.42 nm line 58 . The spectral profile of the line has been recorded at different gas pressures, showing the line broadening with increased pressure. But they didn't provide a broadening coefficient. This probably was due to the large uncertainty they have encountered on determination of the gas temperature from the rotational temperature of N2 emissions. However, an estimated value can be driven from the 2.1 GHz Lorentzian width, reported in Fig. 3 of their publication 58 for the highest studied pressure of 100 Torr, at 30 kHz pulse repetition rate and the gas temperature of Tg=410 K, indicated in their Fig. 5 for the considered conditions. Corrected for the pressure and Tg dependences, we find a pressure broadening coefficient of 19.9 GHz at 1 bar and 300 K. Considering the uncertainty linked to the gas temperature determination, this value, which corresponds to 40 pm, is in relatively good agreement with the 36.3 pm broadening coefficient of the 772.42 nm we have found for the standard conditions.

Table 1 summarize our measured data, the model calculated values and the other published values of our knowledge. Note the larger uncertainties on experimental values relative to the 772.38 nm line, which, due to its weaker absorbance, has its profile partly affected by the wing of the 772.42 nm line profile. The measured ratios of shift/width are comparable to the values reported for argon lines 28,29 , or predicted for the Van der Waals interaction, with Lennard-Jones type potential 59 . The van der Waals widths calculated with equation ( 7) seems to be closer to our measured values rather than those deduced using equation ( 3), yet recommended in 52 and by NIST 54 .

However, this better agreement can be purely fortuitous. Indeed, a realistic calculation of the van der Waals broadening must take into account the real molecular potentials of the interacting atoms, forming Ar*-Ar dimer. Ab-initio calculations on potentials of Ar2 * molecule have been carried out by several groups 60,61,62 . But, to our knowledge, that potentials have never been used for deducing the pressure broadening constants of argon lines. The reason could be the lack of precision on calculated potentials. As an example, in 60, the calculated 0 𝑢 + and 1u potential curves of Ar2* dimer predict an energy difference of 0.00285 Hartree (625 cm -1 ) between them at large atom separation. This should correspond to the energy gap between metastable Ar*(1s5) and resonance Ar*(1s4) states, which is exactly 607 cm -1 , as given by NIST 45 . More, authors of 61 indicate that their calculation predicts the atomic energy levels within 350 cm -1 of the experimental values. Table1. Measured and calculated values (using equations (3) or ( 7)) of the pressure width (FWHM) and shift of the lines. All values are in pm, at atmospheric argon pressure and 300 K.

On relative peak densities of metastable atoms

In low pressure plasmas, the measured [Ar(1s3)]/[Ar(1s5)] density ratio was usually closer to 0.1 63,64,65,66 , rather than to the statistical value (2J3+1)/ (2J5+1)=0.2, where J3=0 and J5=2 are the total angular momentum of 1s3 and 1s5 sates, respectively. The observed enhancement of this ratio with increasing argon pressure, reaching 0.3 at atmospheric pressure, can be related to both smaller reaction coefficient of Ar*(1s3) atoms in 3-body collision with 2 Ar atoms (Eq. 9) (longer lifetime for these atoms) 50 , or to a more efficient production rate of these atoms by collisional transfers from the resonance state Ar(1s2), involving Ar atoms and/or bulk electrons. In fact, the cross-section for electron impact excitation of argon into 1s3 metastable state is about 1 x 10 -22 m 2 , compared to 2 x 10 -21 m 2 for the resonance 1s2 state and 1 x 10 -21 m 2 for both 1s4 and 1s5 states 67 . Thus, e-impact excitation of Ar atoms should strongly overpopulate 1s2 state relative to 1s3. Reported quenching rate coefficients of argon metastable atoms colliding with ground state Ar atoms are 50 : k5=2.1 x 10 -21 m 3 s -1 and k3=5.3 x 10 -21 m 3 s -1 . From the study of Ar collision induced transfers within excited Ar*(2p) and Ar*(3p) states, it was found that transfers with the inner ion core conservation of the excited atom are highly favored 68,69 . As indicated in Table II E is the energy gap between levels, the room temperature value of the transfer coefficient from 1s2 to 1s3 can be deduced as 63 k23=22 x 5.3 x 10 -21 1.2 10 -19 m 3 s -1 and k45=31 x 2.1 x 10 - 21 6.5 10 -20 m 3 s -1 . This Ar-induced transfer of population to 1s3 state would correspond to a decay frequency of 1s2 population density of about 1 and 3 x 10 6 s -1 at 0.321 and 1 bar, respectively. This frequency is comparable to the loss frequency of 1s2 atoms by 3-body reaction forming Ar2* excimer (Reaction 9). In conclusion, at high pressure plasmas, large amount of atoms in the highly over-populated Ar*(1s2) resonance state will be collisionally transferred to its neighboring Ar*(1s3) metastable state, whose direct excitation from the ground state is inefficient. But for the 1s4-1s5 coupled states, first the k45 transfer rate is 3 times smaller than k23; and second, the e-impact production rates of 1s4 and 1s5 states are comparable, thus the 1s41s5 transfers contribution to the net Ar*(1s5) metastable density is much less important.

Besides Ar-induced transfers, e-impact induced transfers can also contribute to the indirect population of metastable states. Rate coefficients in the range of a few times 10 -13 m 3 s -1 have been reported for the e-induced population transfers between resonance and metastable states of Ar(1s) group 70,71 . With an electron density of a few times 10 18 m -3 , the transfer rates will also be in the range of 10 6 s -1 . However, during the discharge pulse, when

Te is larger than the fraction of eV, thus of the energy separation between Ar(1s) states, these transfers should tend to establish a statistical population distribution between the 4 Ar(1s) states. But in the absence of an important inter-gap E-field, the room temperature bulk electrons should preferentially induce down-ward transfers toward metastable states.

On time evolution of Ar*(1s) density

As pointed out before, the analysis of the kinetic of Ar* metastable atoms reveals the presence of a weak production channel for them prior and after the breakdown of the intense discharge current pulse. This channel can be linked to the secondary photoelectron generation from the instantaneous cathode of the DBD by VUV photons emitted from argon excimers Ar2 * formed by reaction (9) [START_REF] Robert | NIST Atomic Spectra Database[END_REF] . Accelerated by the E-field present in the gas gap, these electrons can maintain a discharge current and induce excitation and ionization of ground state Ar atoms. To illustrate this assertion, the time variation of the absorbance when the laser wavelength is set at the maximum absorbance of the 772.42 nm line (corresponding to the maximum density of Ar*(1s3) atoms) is shown in figure 9 for argon pressure of 816 mbar, together with the corresponding discharge current, applied high voltages (Va) and the calculated voltage seen by the gas inside the gap, Vg. As seen in figure 9, the peak of Ar*(1s3) metastable density occurs at tp1.5 µs after the discharge breakdown. Given the about 250 ns lifetime of Ar* atoms at 816 mbar, their density evolution mostly reflects the time variation of their production rate. Thus the observed 1.5 µs delay indicates that from the breakdown up to the Ar(1s) peak density, their production rate largely overpasses their loss rate. At tp=1.5 µs, the discharge current has still 70% of its peak value and Vg has dropped from 1250 V to 570 V. In this range, the voltage seen by the gas gap remains high enough to maintain an efficient production of metastable atoms. But after the Ar*(1s) peak, its loss by 3-body reaction (9) overpasses its e-impact excitation from the ground state Ar atoms. The rate coefficient for excitation to Ar*(1s) states, calculated with Bolsig+ code 72 (Version 12/2017 with Biagi data set) by using the reduced field at the maximum of Ar(1s) peak, is ke 1.5 x 10 -17 m 3 s -1 for Vg=570 V. This is only 4 times smaller than the ke value calculated for Vg-b=1250 V at the breakdown while ke drops to 1.2 x 10 -20 m 3 s -1 for the minimum value of Vg, Vg-m=135 V, reached at tm3.7 µs. At this time, the density of atoms in Ar*(1s) states reaches its minimum, which is about 3 orders of magnitude smaller than its peak value. After tm, both Vg, and Ar*(1s) density again increase, reaching their respective maximum value at ts12 µs. At this secondary maximum, where the reduced electric field becomes again Fs=15 Td, the excitation rate coefficient is increased by 3 orders of magnitude to reach ke 1.5 x 10 -17 m 3 s -1 . We are aware that the amount of Ar*(1s) atoms

produced by e-impact from the ground state to balance their loss by 3-body reaction of Eq. ( 9)

depends also on electron density, which is largely smaller at ts12 µs than at tp1.5 µs. This is the reason why for the same Vg=570 V, thus similar ke1.5 x 10 -17 m 3 s -1 , the Ar*(1s) atoms density is almost 2 orders of magnitude smaller at ts12 µs than at tp1.5 µs. This is also the explanation of the non-measurable Ar(1s) density when the voltage amplitude increases in the following half cycle as the electrons trapped in the positive column are drifted to the anode when the Vg polarity is reversed.

In conclusion, argon atoms in metastable states can be produced outside the discharge current pulse which follows the breakdown. The electric field, resulting from the externally applied voltage and charges accumulated in the internal surfaces of dielectrics during the discharge pulse, is high enough for heating electrons, giving them a mean energy of a few eV.

This E-field, whose amplitude is well below the necessary E-field to induce a breakdown, is, however, high enough for maintaining a weak excitation in the gas. Nevertheless, looking on figure 8, a question arises: why a distinctly observed secondary maximum on Ar* metastable density is only present at 816 mbar argon pressure? This peculiarity can be attributed to the more significant enhancement at this pressure of Vg, then of the E/N in the gas gap, between their minimum values Vg-m and their secondary maxima, Vg-s. To illustrate the point, values of Vg-m and Vg-s on the five studied gas pressures are reported in Table 2, together with reduced field values corresponding to them. We note that the most significant enhancement on E/N between the minimum and the secondary maximum of Vg occurs in 816 mbar plasma. Also, in 1 bar plasma, E/N remains moderately high, evolving from 6 to 13 Td between these two positions. As a consequence, in this plasma, a weak production channel of Ar* atoms maintains their density to none zero value during that period. As was pointed out before, for each pressure, the amplitude of the applied HV was adjusted for obtaining stable and reproducible discharges, but at the lowest possible voltage to limit the electron density. Table2. Amplitude of the applied voltage (Va-m) and the voltage in the gas gap at its minimum (Vg-m) and secondary maximum (Vg-s) at studied gas pressures. E/N values corresponding to Vg-m and Vg-s are also given. Uncertainties on reported V and E/N values are less than 10%.

Acknowledgments

The work was supported by the Agence Nationale de la Recherche through the Investissement d'avenir program (ANR10LABX2201). The "Réseau des Plasmas Froids" of CNRS/MRCT (France) is acknowledged for providing the DFB diode laser and the travel support for Nader Sadeghi. The authors thanks Gerjan Hagelaar for his advices in using Bolsig+ code and Serge Béguier for his contribution to the double Voigt fit of profiles.

Figure 1 .

 1 Figure 1. V-I characteristics of the DBD discharge at three pressures inside the chamber. The current density, Idech is deduced by subtracting the displacement current from the total current and Va and Vg are the voltage applied to electrodes and in the gas gap, respectively.

Figure 2 .

 2 Figure 2. Experimental (circle) and simulated spectra with Tg=305 K (solid line) of (4→1) and (5→2) bands of the 1 st positive system of nitrogen with 0.04% N2 added to atmospheric pressure argon DBD plasma. Arrows show the argon 667.73 nm (fully saturated) and 675.28 nm lines positions.

shown in figure 3 .

 3 The laser beam from the DL passes through a beam-splitter (BS) which provides two secondary beams. One of them goes through a low-pressure argon discharge reference cell (RC) and is detected with a silicon photodiode (PD1). The other secondary beam crosses a 20 cm long confocal Fabry-Perot interferometer (FPI) and is detected by PD2. The mode-hop-free functioning and the linear frequency change of the DL versus its temperature, are controlled from the regularity of the transmitted peak of the FPI. The absorption signal from the low-pressure Ar discharge cell permits to localize the non-shifted central wavelength, 0 of the lines. The main laser beam goes through the DBD device and is detected by a fast silicon photodiode, backed with a trans-impedance amplifier PD3 (New Focus 1801, 125 MHz bandwidth and G=40V/mA), which provides 3 ns temporal resolution. A diaphragm limits the laser beam diameter to about 1 mm inside the DBD and appropriate optical attenuators on the path of the beams reduce the laser intensities to avoid optical saturation in the DBD and in the low-pressure argon cell plasma. Signals from all three PDs are recorded with a 400 MHz bandwidth digital oscilloscope (Lecroy 44Xi) triggered in phase with the HV waveform, averaged over 2000 cycles of the HV and hence stored for the data processing. 1001 data points, with a time interval of 50 ns are taken during the 50 µs period of the HV. Thus the final time resolution of the records is 50 ns.

Figure 3 .

 3 Figure 3. Experimental setup used for determination of Ar metastable atoms densities by absorption spectroscopy using a tunable diode laser. PDs represent photodiodes.

  For each argon pressure, about 50 TVTLS have been recorded in the 772.35 to 772.47 nm interval by changing the temperature of the diode laser by fixed steps of about 5 mK. Calibrated from the 375.0 MHz free spectral range (FSR) of the FPI and the precise 44.66 pm wavelength gap between the two studied argon lines 45 , the precise wavelength interval between the successive acquisition steps is =2.180±0.025 pm (corresponding to =1.096±0.013 GHz). In figure4are reported some of the recorded signals from PD3 for 312 mbar argon pressure. The origin of the time is the same as in Fig.1and corresponds to the start of the fast discharge current increase in the positive half-period of the HV and signals after t=25 µs are relative to the 2 nd discharge pulse on the negative half-period of the HV. Only the time-varying parts of the recorded data are shown in this figure. Emission signal from the DBD plasma, E(t) is also shown in the bottom of the figure and its amplitude before the start of the discharge pulse (t<0) is the offset of the detector, the background (BG). Plasma emission pulses are in accordance with the discharge current pulses.

Figure 4 .

 4 Figure 4. Signals from PD3 during the most significant parts of one HV period at Ar pressure of 312 mbar. Note breaks on both time and amplitude axis and different scales for the emission (laser blocked) and laser ON signals. Step 31 is when the laser wavelength is at the maximum absorption of the 772.42 nm line and the following steps are with the laser

Figure 5 .

 5 Figure 5. Reconstructed absorption profiles at the peak absorbance (A) and 2.75 µs later (B) in 455 mbar DBD plasma, presented with the Voigt profile fits of 772.376 (dashed blue) and 772.421 (dashed red) nm lines. The wavelength step of the DL scan is =2.18 pm.

Figure 6 .

 6 Figure 6. Reconstructed absorption profiles at five argon pressures between 312 and 1000 mbar. The wavelengths' origin is the non-shifted spectral position (at low pressure) of

Figure 7 .

 7 Figure 7. Pressure dependence of the respective Lorentzian widths (FWHM) and shifts of studied lines, deduced from fitting of their absorption profiles with Voigt functions.

x10 7 s - 1 ,

 1 taken from 45, the calculated values of absorption coefficients, are k5=1.47 x10 -28 m 3 and k3=1.66 x10 -27 m 3 . With L=0.05 m and the integrals of V5() and V3(), coming from the fit of the absorbance curve, the deduced peak densities decrease from N5=3.8 x10 17 m -3 and N3=7.5 x10 16 m -3 at 312 mbar to N5=1.2 x10 17m -3 and N3=3.8 x10 16 m -3 at atmospheric pressure. As was pointed out in section 4, the laser position inside the gap and the amplitude of the HV were adjusted at each pressure to obtain the largest absorbance. Therefore, no significant conclusion can be deduced from the diminution of the peak metastable densities when increasing the pressure. However, we have also observed a monotonical decrease of the ratio of peak densities N5/N3 from 5.1 at 312 mbar to 3.3 at atmospheric pressure. This evolution could be assigned to the more efficient excimer formation reaction from Ar*(1s5) atoms than from Ar*(1s3) metastables. The reported rate coefficients for the corresponding 3-body reaction:Ar * +Ar + Ar → 𝐴𝑟 2 * + 𝐴𝑟(9)are 1.1±0.4 x10 -44 m 6 s -1 and 0.83±0.3 x10 -44 m 6 s -1 for Ar*(1s5) and Ar*(1s3) atoms, respectively50 . Corresponding decay times of 1s5 (1s3) metastable atoms by reaction (9) would be 0.16±0.06 µs (0.21±0.08 µs) and 1.67±0.6 µs (2.2±0.8 µs) at 1000 and 312 mbar, respectively. However, the recorded time variation of metastable atom densities after the discharge breakdown, shown in figure8, does not seem to confirm this prediction. First, as expected, the metastable atoms densities decay exponentially after the peak of the discharge current. But the measured decay time of about 1.15 µs at 312 mbar is shorter than the calculated 1.7 µs with the rate coefficient of ref 50. At the opposite, the decay times measured at 1 atmosphere: 1 µs for Ar*(1s5) atoms and 0.7 µs for Ar*(1s3) atoms, are much larger than the calculated 0.2 µs decay time. Also, a secondary peak of metastable density is clearly visible in 816 mbar plasma and one observe an apparent production of excited atoms after the end of their initial fast decay at t≥4 µs, at 1 bar.

Figure 8 .

 8 Figure 8. Time variation of absorbances ( to metastable densities) at different argon pressure. The time origin is the start of the fast discharge current increase at the positive half-period of the HV (for Ar*(1s5) atoms) and at the negative half-period of the HV (for Ar*(1s3) atoms).

Figure 9 .

 9 Figure 9. Time variation of applied voltage Va (black), the voltage Vg seen by the gas gap (red), discharge current (green), and the absorbance when the laser is set at the maximum absorption by Ar*(1s3) metastable atoms (blue) at 816 mbar argon pressure. The time origin is the start of the fast increase of the discharge current at the positive half-period of the HV. Note the logarithmic scale for the 772.42 nm line absorbance.

  . Also, Nayak et al have recently applied the broad-band absorption spectroscopy technique for measuring the pressure broadening coefficients of 750.39, 751.47, 763.51 and 794.82 nm argon lines

  IAr are the ionization potentials of hydrogen and argon atoms, Ei is the energy of the upper or lower state of argon to which the observed transition belongs and li is the orbital angular momentum of the optical electron of the state.

	The active electron of the upper state of 772.38 nm Ar(1s5-2p7) line is in p orbital,
	thus lu=1 and in the lower state the electron is in s orbital, with ll=0. In equation (4), replacing
	energies by their respective values 45 one can deduce Ru 2 =55 and Rl 2 =33.1, which finally lead
	to C6u-C6l=3.52x 10 -32 . These values introduced in Eq. (3) provide vdW=25.8 pm at 1 bar and
	300 K for the 772.38 nm line.
	For 772.42 nm Ar(1s3-2p2) line, the orbital angular momentum of active electrons
	are again lu=1 and ll=0, resulting in Ru 2 =64.2 and Rl 2 =30.1, which lead to C6u-C6l=5.48x 10 -32 ,
	resulting finally in vdW=31.0 pm at 1 bar and 300 K for this line.
	Δ𝜆 𝑣𝑑𝑊 [𝐴𝑟]	=	𝜆 2 𝑐	.	4𝜋 3	. [𝛼 𝑝 .	𝑒 2 .𝑎 0 2 ℎ	. (𝑅 𝑢 2 -𝑅 𝑙 2 )] 2/5
					𝐼 𝐻 𝐼 𝐴𝑟 -𝐸 𝑖	) 2	. [1 +	𝐼 𝐴𝑟 -𝐸 𝑖 5.𝐼 𝐻

. (1 -3. 𝑙 𝑖 . (𝑙 𝑖 + 1))]

(4)

where IH and If instead of using equation (

3

) recommended by Physicist's Desk Reference52 and by

NIST

54

, we start from the quantum-mechanical theory of hard sphere collisions, developed by

Cowley

[START_REF] Cowley | The Theory of Stellar Spectra[END_REF]

and described in Ref.

25

, we can write:

  Thusat this state, it is not possible to analyze the influence on Vg-m and Vg-s of the applied HV amplitude, Va-m. A systematic study of the time evolution of Ar* atoms density and of Vg when varying the amplitude of the HV, would certainly help for getting a better insight on physical processes responsible for the production of Ar* metastable atoms outside the discharge current pulse initiated by the breakdown.

	Pressure (mbar)	312	455	678	816	1000
	Va-m (V)	795	950	1350	1680	1780
	Vg-m (V)	97	50	106	136	300
	Vg-s (V)	120	134	320	570	645
	E/Nm (Td)	6.5	2.5	3.3	3.5	6
	E/Ns (Td)	8	6	10	15	13
	.