dataesr/scientific-paragraphs-categorization huggingface dataset:
These can be forecast models  [25, 26]  or reanalysis of global meteorological models  [27] [28] [29] , usually stored as 4D meteorological datasets. As discussed by Ref. [20] , significant improvements in the modelling of tephra transport, dispersal, and sedimentation have been put forward over the past years, such as: (a) the implementation of satellite data assimilation techniques to improve the real-time particle tracking; (b) the use of ensemble probabilistic forecasts to account for eruptive source parameters uncertainty; or (c) the improvement of the computational efficiency of numerical models to reduce computational times. Nevertheless, several mechanisms that can highly influence tephra transport, dispersal, and sedimentation are still poorly considered or neglected in the models used operationally and in hazard-related studies.
For instance, particle aggregation  [30] [31] [32]  has been implemented only sporadically in numerical models, e. g. ,  [33] [34] [35] , while other broader scale, en masse depositional mechanisms such as ash fingering  [36] [37] [38]  or sediment waves  [39]  have not been included in any model to date. Moreover, the employment of different meteorological datasets with different spatiotemporal resolutions and different atmospheric parameters could lead to great differences in simulation outputs, even if the source conditions are the same  [40]. Numerical models have become a crucial tool for managing the tephra hazard in real time and understanding related processes  [20]. Still, it is necessary to acknowledge the above-mentioned limitations, study their impact on the results, and identify potential areas of improvement.
5 ± 1. 0 × 10 11 kg  [56]. With these values, this eruption was classified as sub-Plinian with a VEI of 3-4 by  [57]. Finally, Ref. [53]  calculated the total grain size distribution (TGSD) of Unit I in the range -4Φ/11Φ, using different datasets and methods (i. e. , Voronoi tessellation, weighted average of samples, and mass of individual Φ sizes). Globally, main results indicated that: (a) TGSD has a bimodal distribution with the two sub-populations (with modes at -2Φ and 7Φ) separated by the 3Φ grain size; (b) the fine subpopulation is associated with sizeselective sedimentation processes (e. g. , particle aggregation, convective instabilities); and (c) grain size bimodality is related to a significant lack of particles in the 3Φ size. This eruption has been the focus of multiple studies which compared the observed and modelled values of: (a) column height [40]; (b) column mass load (i.
Finally, Ref. [53]  calculated the total grain size distribution (TGSD) of Unit I in the range -4Φ/11Φ, using different datasets and methods (i. e. , Voronoi tessellation, weighted average of samples, and mass of individual Φ sizes). Globally, main results indicated that: (a) TGSD has a bimodal distribution with the two sub-populations (with modes at -2Φ and 7Φ) separated by the 3Φ grain size; (b) the fine subpopulation is associated with size-selective sedimentation processes (e. g. , particle aggregation, convective instabilities); and (c) grain size bimodality is related to a significant lack of particles in the 3Φ size. This eruption has been the focus of multiple studies which compared the observed and modelled values of: (a) column height [40]; (b) column mass load (i. e. , the integration of the mass of the ash cloud along the atmospheric vertical levels;  [51, 58] ); and (c) ground deposit measurements (thickness and mass loading,  [52, 59] ); mass loading and grain sizes [40].
The PLUME-MoM/HYSPLIT Model For this work, we used the integral plume model PLUME-MoM and the particle transport and dispersion model HYSPLIT, as already performed by Refs. [4, 40] , coupled through a suite of Python scripts (see "Data Availability Statement"). First of all, the column model is initialized with a meteorological profile extracted at the vent location by HYSPLIT from the meteorological datasets. Then, the mass lost from the plume edges at intervals of fixed height and that reaching the neutral buoyancy level are processed to define the source locations and rates for HYSPLIT. In this paper, we use a newly released version of PLUME-MoM (PLUME-MoM-TSM,  [33] ). As in the first version of Ref. [60] , PLUME-MoM solves the equations for the conservation of mass, momentum, energy of the gas-particle mixture, and for the conservation of mass of the individual phases (solid particles and gas components).
It is important to observe that aggregation depends on the particle-particle interactions, and thus on their volumetric fraction within the volcanic column and cloud. While at lower levels in the column the solid fraction is large enough to favor aggregation, higher in the column and in the cloud this is less likely, and thus modeling aggregation only within the column represent a good approximation of the real phenomenon. We also tested 4 different meteorological datasets (Table  1 ): (1) the ERA-Interim [27] and (2) the ERA5 reanalysis data  [28] , both elaborated by the European Centre for Medium-Range Weather Forecasts (ECMWF); (3) the NCEP/NCAR Global Reanalysis Data  [29]  and (4) the Global Data Assimilation System (GDAS) archive  [26] , both developed by the National Oceanic and Atmospheric Administration (NOAA).
The main differences   [52]. Isomass line values  [55]  are in kg/m 2. Coordinates expressed in the WGS84 coordinate system. Service Layer Credits, courtesy of: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AeroGRID, IGN, and the GIS User Community. The along-axis reconstructed test sites are also used to define transects orthogonal to the dispersal axis (Figure  2 ), which are in turn the basis to estimate the total mass deposited within such transects, both from field data and from simulations. To do so, within a GIS environment we used the isomass lines (both those from field data and those produced after the simulations) converted into polygons, whose areas are multiplied by the value of the isomass line itself. We also tested 4 different meteorological datasets (Table  1 ): (1) the ERA-Interim [27] and (2) the ERA5 reanalysis data  [28] , both elaborated by the European Centre for Medium-Range Weather Forecasts (ECMWF); (3) the NCEP/NCAR Global Reanalysis Data  [29]  and (4) the Global Data Assimilation System (GDAS) archive  [26] , both developed by the National Oceanic and Atmospheric Administration (NOAA).
[40]: the GDAS meteorological dataset (Table  1  from this study) and the Ganser settling velocity model (see Appendix B). In particular, the latter two have been chosen because: (a) the GDAS dataset is one of the two released by NOAA (along with the NCEP/NCAR Reanalysis, see Table  1 ) that could be employed in HYSPLIT without format conversion (as necessary for ERA-Interim and ERA5, see Table  1 ), and the one among the two with a better repro-duction of past eruptions (see  [40] ); (b) the Ganser settling velocity model  [61]  is one of the default models used in HYSPLIT and the only one originally present in both models. The complete list of parameters used for such simulations is available in Table  S1  from the Supporting Information. We show in Figure  3  the along-axis differences (every 10 km) in grain size distribution for the four simulation types.
Effect of Different Settling Velocity Models In addition to the simulations presented in the previous section, we performed three further simulations in which we have considered (in both PLUME-MoM and HYSPLIT) the three settling velocity models detailed in this study (Ganser, Pfeiffer, and Textor; see Appendix B). For such simulations (named NA, NAP, and NAT, respectively-see Table  3 ) we have not considered aggregation and we have used the same set of parameters as Table  S1  and the GDAS meteorological dataset (Table  1 ) for the same reasons specified in Section 4. 1. We have compared the simulated values with those deriving from field data of: (1) the total mass deposited in each transects defined in Section 3. 1 (Figure  4a-d);  (2) the mass loading values at the sampling points of Ref.
e. , with the lowest T 2 ) for the whole sampling point dataset (Inv-NA) and the subset of sampling points < 80 km (Inv-NAProx). For comparison, we also include the T 2 values of the NA single simulation of Figure  4c  which, among the three cases described in Section 4. 2, is the one with the lowest T 2  Total value. Atmosphere 2022, 13, x FOR PEER REVIEW 13 of 28   For the two simulations with the lowest T 2 values of Table  3  (whose parameters are listed in Table  S2  from the Supplementary Material) we have calculated (Figure  6 ): (1) the total mass deposited in each transects defined in Section 3. 1 (Figure  6a-c);  (2) the comparison simulated/observed mass loading values at the 75 sampling points of Ref. [56]  for which there is a mass loading measure (Figure  6d ); and (3) the comparison simulated/observed median grain size (MdΦ) at the 24 sampling points of Ref.
[56]  for which there is a grain size analysis (Figure  6e ). The T 2 values of Table  4  show that the inversion procedure allows us to significantly improve the agreement between simulation results and observations, as shown by the large decrease in T 2  Total values (from 561 to 168, see Table  4 ), especially those related to mass loading (ML). This is also reflected by the lower values of mass for each transects and in total (Figure  6c ) as compared to Figure  4d. The total mass overestimation with respect to field data is still by a factor of 2 (2. 26 and 1. 93 for Inv-NA (best) and Inv-NAProx (best), respectively). Regarding mass loading (Figure  6d ), the number of sampling points falling within the limits of a factor 5 of field observations are 68% for the whole dataset (Inv-NA, 75 data points) and as much as 85% for the subset of 56 sampling points within 80 km from the vent (Inv-NAProx).
For the best inversion simulations we have also evaluated the modeled versus observed median values of the grain size distribution (MdΦ) for all the sampling points (Figure  6e ), given the better results related to the reproduction of the total mass (Figure  6c ). For the best-fitting scenario, for 54% and 67% of the sampling points, respectively, within 120 km (13 out of 24, Inv-NA) and within 80 km (12 out of 18, Inv-NAProx), the simulated median values are comprised within ±1 Φ with respect to those from field observations. The results obtained from this set of simulations are presented with correlation plots (Figures  7  and 8 ), which are helpful to investigate the dependence between multiple variables at the same time and to highlight the most correlated variables in a data table. In our case, we are investigating the dependency between the T 2 minimization function and (a) the three settling velocity models and the eight continuous parameters related to particle properties and eruption features (Figure  7a ), (b) the four meteorological datasets and the eight continuous parameters related to particle and eruption features (Figure  7b ), and (c) the five parameters that control diffusion in HYSPLIT (Figure  8 ).
Effect of Initial Water, Dry/Wet Aggregation, and Different Settling Models Regarding instead the two sets of discrete parameters that compose Figure  7  (i. e. , settling velocity model and meteorological dataset): (1) the Ganser settling velocity model provides the smallest range of variation of the T 2  Total values up to ~4000, while the other two reach similar higher values up to ~8000; (2) the NCEP/NCAR meteorological dataset provides the greatest T 2  Total values, while the other three (GDAS, ERA-Interim, and ERA5) have the same range of variation of T 2  Total values. The correlation plots between the T 2 function and the parameters that control diffusion in HYSPLIT (Figure  8 ) show instead that all of these parameters provide a very similar range of variations of the T 2 function.
In general, for simulations NA, NAP, and NAT where default values from the literature are used (Table  S1 ;  [40, 53, 56, 57] ), the total deposited mass up to 120 km from the vent is much higher in the simulations compared to observations (Figure  4d ). Between the simulations performed with the three settling velocity models (NA, NAP, and NAT) and field data, we observe a difference of a factor of 3, with a slightly better value considering the Textor model. Such large differences between field and modelled data cannot be ignored, and highlight that model calibration and evaluation should also consider this parameter (i. e. , total mass deposited) to have a clear understanding of the capabilities and to identify how to improve the model itself. Differences in total mass between model and deposit are especially high between 20 and 60 km from vent.
Mass overestimation of the model in the different transects is now reduced up to two times more than field data, but is still considerable (Figure  6c ). In the absence of similar comparison with other models, this discrepancy should be therefore considered if PLUME-MoM/HYSPLIT is used to derive, for instance, hazard maps. Among the inverted parameters, we highlight that for the two simulations with the lowest T 2 values in Table  4  the corresponding settling velocity model is that of Ganser, while the meteorological datasets are ERA-Interim and ERA5, respectively. The former is consistent with experimental data where the Ganser settling velocity model has been considered a good approximation for real particles (see, for instance,  [36] ). Regarding the meteorological datasets, ECMWF products (i.
e. , ERA-Interim and ERA5) appear to provide a better reproduction of the real deposit. However, we note that such datasets are more difficult to be employed in HYSPLIT (due to conversion issues from a different file format) and do not systematically provide the best results for all eruption types (see  Section 5. 3 and [40, 51] ). The employment of a subset of sampling site (Inv-NAProx) is also useful to produce an overall improvement of the total mass deposited (see Table  4  and Figure  6c, d ). Due to the better reproduction of the total mass deposited, for only these two simulations (Inv-NA and Inv-NAProx) we have also evaluated the difference with respect of field data of the median of the grain sizes (MdΦ, Figure  6e ). This parameter is the most difficult to be reproduced by numerical model  [40] , and in our case there is a slightly better reproduction of the best simulation of the Inv-NAProx set (although there is a lower amount of sampling points).
• Ganser is recommended as the best choice for modelling settling velocity, as the variation of the T 2 function is lower compared to Textor and Pfeiffer (Figure  7a ). A possible explanation for the best results obtained using the Ganser model is related to the amount of particles with regular and rounded shapes which, as shown by Ref. [56] , make up 72 to 93 wt% of the particles within the deposit of Unit I (see Section 2. 1). This type of particle has been shown by Ref. [36]  as being well described by the sphericity (i. e. , the shape factor ψ, see Appendix B). In turn, this parameter is considered to be well suited for the accuracy of the Ganser equation (see  [73] ); • the NCEP/NCAR meteorological dataset is less accurate in reproducing the plume height and final deposit as compared to the other datasets, which instead produce a more or less equal variability (Figure  7b ), and a high degree of uncertainty should be therefore considered if it is employed.
A possible explanation for the lower accuracy of the NCEP/NCAR dataset is linked to the lower number of vertical pressure levels and by its low spatial (and temporal) resolution (see Table  1 ). Such low-quality features, as compared to the other datasets, do not allow for an optimal representation of smallscale atmospheric variability and therefore for good tephra dispersal representation. Finally, considering the five parameters that control diffusion in HYSPLIT (see Figure  8 ), the quasi-similar variability of the T 2 function for all the possible configurations of such parameters suggest that it is possible to use the default values proposed in the user's guide (https://www. arl. noaa. gov/documents/reports/hysplit_user_guide. pdf, accessed on 11 May 2018).
• The parametric analysis (performed with additional 900 simulations with the same minimization function) highlighted a primary control exerted by the mass eruption rate on the model outputs, while the other parameters influence the outputs to a lesser degree. The Ganser settling velocity model produced a lower variability in the minimization function, and is therefore more indicated as a default option. On the other hand, the meteorological dataset that produced the largest variability in the minimization function is the NCEP/NCAR Reanalysis (which therefore has a large impact in the final outputs of the model and is not suggested to be employed), while the others produced similar variability. The parameters that control diffusion in For the first model  [61] , an initial value of settling velocity (w ST ) is calculated for the Stokes regime (Reynolds number Re << 0.
Funding: This research was funded by the  French Government Laboratory of Excellence  initiative n •  ANR-10-LABX-0006 , the  Region Auvergne  and the  European Regional Development Fund  ( ClerVolc project-Programme 1 "Detection and characterization of volcanic plumes and ash clouds "). This is Laboratory of Excellence ClerVolc contribution number  538. This research was also partially financed by the  French government IDEX-ISITE  initiative  16-IDEX-0001  ( CAP 20-25 ).
Data Availability Statement: PLUME-MoM-TSM and the scripts for its coupling with HYSPLIT are available at https://github. com/demichie/PLUME-MoM-TSM, accessed on 11 May 2021. The digital object identifier (DOI) for the version of the code documented in this paper is https:// doi. org/10. 5281/zenodo. 3904379, accessed on 11 May 2021. HYSPLIT (for LINUX) is available at https://www. ready. noaa. gov/HYSPLIT_linux. php, accessed on 11 May 2018.
Atmosphere 2022 , 28 Figure 7. 2022287 Figure 7. Correlation plots of two discrete parameters (settling velocity model and meteorological file dataset) and eight continuous parameters (initial water content, mass eruption rate, exit velocity, initial temperature, initial/final values of the density profile of the particles, heat capacity, and particle shape factor) with respect to the T 2 minimization function (see Sections 3. 2 and 3. 3). In (a), the sensitivity is analyzed with respect to the different settling velocity models while in (b) with respect to the different meteorological datasets. In each panel: on the left, the T 2 function is shown with respect to the discrete variables, colored boxes contain values between the 25th and 75th quantiles, and horizontal dashed lines represent the median and vertical solid black lines extends up to the minimum and maximum values; central graphs show the variation of T 2 with respect to the continuous parameters (color code is the same as in the left panel, grey dashed lines are the overall trends of the distributions); and the graph on the right is the distribution of the T 2 function values for the 900 simulations.
6 0. 7 Ganser Settling velocity Settling velocity model considered PM/HY m/s D Textor - - Pfeiffer GDAS Meteorological file Meteorological dataset considered PM/HY - D NCEP/NCAR ERA-Interim - - ERA5 K mix0 Minimum mixing depth HY m D Every 100 m 100 500 K zmix Vertical Mixing Profile HY - D Varies with height Single average value - - K def Horizontal Turbulence HY - D Proportional to vertical turbulence From velocity deformation - - K bls Boundary Layer Stability HY - D Heat/momentum flux Wind/temperature profile - - Beljaars/Holstag K blt Vertical Turbulence HY - D Kantha/Clayson - - Velocity variance.
Estimation on real data At least seven sensors are required (section 3. 3. 2. ) to use the MUSIC algorithm adapted to the Model M2. As mentioned in section 3. 4, we only had five sensors. The sensors were moved to perform successive measurements. The different measurements are then not synchronized. Therefore, our estimator, based on MUSIC, cannot be used on these measurements. However, results evaluated from the delay times between the sensors are presented in Figure  20  (black curve). These delay times obtained after retiming, introducing additional errors. The criterion presented here is the inverse of the squared error between the estimated delay times and the delay times calculated by the Model M2. The values of the criterion are obtained by varying the variables to be estimated: the depth (SZ), the velocity inside the trench (V0) and the velocity outside the trench (V1).
Acknowledgments: We would like to thank the  Laboratory of Mechanics and Acoustics (LMA -CNRS), Marseille, France. We also express our sincere gratitude to  Cédric Pinhède , research engineer at LMA, who allowed us to access the anechoic chamber of LMA and to qualify our loudspeaker. We gratefully acknowledge  S. Operto  for providing the wave propagation finite difference modelling code used in this study.
The risk of metallic armour melting constitutes a major concern for ITER and DEMO. Combined computational and experimental effort has led to a successful understanding of melt dynamics in present-day tokamaks, but there remain unexplored melting regimes of relevance to future reactors. Analysis of recent poor-versusefficient thermionic emitter sample exposures in ASDEX-Upgrade and ITER-like actively cooled tungsten leading edge exposures in WEST is presented. The coupled thermal response and melt dynamics is modelled with the new MEMENTO code employing the MEMOS-U physics model which has no adjustable parameters. In the weak Lorentz force regime accessed in the exposures, very close agreement between modelling and experiments is achieved not only for the deformation profiles, but also for the additional, unique to these experiments, constraints; simultaneous thermal response of two different materials in ASDEX-Upgrade and in-situ detection of melt build-up in WEST.
The assessment of the overall deposited energy uncertainty, as recovered by IR thermography, can be facilitated by a comparison with thermo-couple (TC) data from the outer divertor. In the discharge analysed here, the total energy onto the entire lower divertor is 3. 8 MJ as determined by the IR measurements and 4. 8 MJ as determined by the TC data. Accounting for the symmetric TC data error-bar of ∼ 20%, this translates to a possible underestimation of the IR-recovered power flux up to ∼ 50%. We restrict the analysis to loading in the optical approximation; this way to induce Ir melting the experimental heat flux needs to be further increased by ∼ 40%. It is worth underlining that this flux deposition strategy underestimates the overall energy received by the sample. The geometry of the sample (Fig.
While the matching of the final deformation profiles constitutes the principle part of the experiment-simulation comparison, the design and diagnostics of these exposures also led to experimental constraints which further enhance the value of the validation effort. In particular, in the AUG experiment, it has been shown that the MEMENTO code implementation of the MEMOS-U physics model was able to reproduce the thermal responses and deformation profiles of two different materials (Ir and Nb), which possess diametrically opposite thermionic properties, under the same experimental heat flux. Furthermore, the timing of formation of the sustained Ir melt pool revealed by the simulations entirely agrees with the results of four Ir exposures, where only the last and the longest one had induced observable melt volume and displacement.