dataesr/scientific-paragraphs-categorization huggingface dataset:
2 and 2. 3. The comparison with the neutron elastic scattering cross sections calculated with a Free Gas Model approximation highlights the large differences between the formalism, which may introduce biases in neutronic calculations. For example, the use of the Free Gas Model can imply a bias of about 100 pcm (0. 1%) on the neutron multiplication factor    calculated for integral benchmarks with UOX fuel. Such a bias cannot be seen as a negligible source of uncertainties, given that the total uncertainty on the calculated    should be lower than 500 pcm (0. 5%). 1 O in UO 2 (b) as a function of the incident neutron energy at  = 300 K. The inelastic and coherent elastic scattering cross sections were calculated with the CINEL code by using equations presented in Sections 2. 2 and 2. 3. The neutron cross sections calculated with the Free Gas Model are plotted for comparison.
Calculation scheme The calculation scheme used in this work are summarized in Fig. 6. The first step consists in producing with the CINEL processing tool an application library that contains temperature-dependent neutron scattering cross sections. CINEL has been developed in Python in order to take full advantages of the latest CPU and GPU accelerated libraries. The neutron scattering cross sections are stored in ascii files by following the ENDF-6 format requirements for thermal scattering laws  [26]. The second step consists in simulating the neutron diffraction experiments with the Monte-Carlo code TRIPOLI4 ®. The high performance computing capabilities allow to reach a relative statistical uncertainty of about ±0. 5% on the top of the Bragg peaks (and ±5. 0% in between) in a few minutes for a given temperature.
Validation of the coherent elastic scattering formalism The experimental validation of our calculation scheme (Fig. 6 ) was performed thanks to the neutron diffraction patterns of Ruello et al. [3]  measured with the D20 diffractometer by using an incident neutron energy of  = 48. 05 meV. As shown in Fig. 1 , the contribution of  the inelastic scattering cross sections around this energy is rather low. Therefore, the Ruello's data are suited to verify the implementation of the coherent elastic scattering formalism (Eq. (  14 )) in the CINEL processing code and its subsequent use in tripoli4 ®. No attempt was made to determine the UO 2 cell parameters as a function of the temperature. Such a work was already performed by Ruello  [20]. His results are shown in Fig. 3. Only experimental correction parameters involved in Eqs.
Biases due to theoretical approximations would need to be investigated. The performance of our calculation scheme was also investigated by simulating atomic pair distribution functions to probe the structure of UO 2 at elevated temperature. The differences observed at 1273 K between the experiment and the theory confirm that the local deviations of the oxygen atoms from the average structure of UO 2 are not compatible with an ideal fluorite structure. We show that the CINEL processing tool offers the possibility of testing atomic disorder configurations, anharmonic models or space groups which are suggested in the literature for exploring the unexpected shortening of the U-O distance with increasing temperature. The neutron cross sections for UO 2 , calculated with the processing tool CINEL, will be delivered at the JEFF project of the OECD/NEA databank.
, 1998)  or higher  (Selesnick et al. , 2007)  energy protons. In this paper, we use results from Salammbô simulations improving from  Maget et al. (2008) , using direct data assimilation from NOAA GOES data and an improved energy-dependant magnetic shielding model to estimate the trapping of SEP protons, as presented in Section 2. 2 of this paper. A relatively low number of missions have been measured the proton radiation belt in the MeV energy range. The SEM2 MEPED  (Yando et al. , 2011)  detector on-board the NOAA POES constellation since 1998 has three available channels covering this range (0. 8-2. 5 MeV, 2. 5-6. 9 MeV, and >6. 9 MeV), providing a long-term sampling of the radiation belts in low earth orbit (LEO). Likewise, on GEO, the NOAA GOES constellation has provided three proton channels  in this energy range since 1974, although with some variation in the measured energies across the different missions.
A sampling of the equatorial regions below GEO, which is of main interest for EOR missions, has been sporadic. The CRRES PROTEL  (Violet et al. , 1993)  instrument has provided good measurements in this region during less than two years in 1990 and 1991. This data has been extensively used to study the dynamics of the proton belt  (Hudson et al. , 1995; Gussenhoven et al. , 1996; Lozinski et al. , 2019). The solid-state telescopes (SST) onboard the THEMIS constellation  (Angelopoulos, 2009)  have provided proton measurements since 2007, but it showed severe contamination in the MeV energy range due to electrons  (McFadden et al. , 2009). The TacSat-4 satellite has also featured a proton monitor (CEASE) and a solar cell degradation experiment  (Jenkins et al. , 2013). Most recently, the Van Allen Probes mission  (Spence et al.
, 2013)  has featured several proton monitors and sample the proton radiation belt in a large range of energies. In particular, the RBSPICE instrument provides 24 ions channels between 1 MeV and 10 MeV  (Mitchell et al. , 2014). These various datasets have shown an important variability of the proton belt at these energies at various temporal scales  (Johnston et al. , 2012 (Johnston et al. , , 2015)) , which is hard to account for in specification models. In particular, the radiation belt during solar cycle 24 is largely more extended than during the previous two solar cycles due to the low geomagnetic activity in the past decade. The high variability of the radiation belt state is easily illustrated by the NOAA POES 15 measurement of the 2. 5-6. 9 MeV protons, as shown in Figure  1. The standard AP8 model  (Sawyer & Vette, 1976) , widely used in the industry as a specification model for spacecraft design, only provides two states linked to the solar cycle minimum and maximum and does not accurately represent the wide variability seen at smaller timescales.
The ONERA Middle-Energy Proton for EOR (OMEP-EOR) is based on flux maps generated from the RBSPICE data. When insufficient data was available, we used simulation data from the Salammbô model to fill the gaps. A statistical spatial and temporal model was fitted on this dataset, which allows the estimation of the average flux statistical distributions for arbitrary spacecraft trajectories. The paper is organized as follows. In Section 2, we describe the experimental and simulation data used for the development of this model. The model development is then detailed in Section 3. Finally, model runs and validation are presented in Section 4. 2 Data used in this study.
Van Allen Probes RBSPICE data The model developed in this study is based on data from RBSPICE on board the Van Allen Probes  (Spence et al. , 2013; Mitchell et al. , 2014). The RBSPICE data (level 3) have been downloaded from the RBSPICE website (http://rbspicea. ftecs. com). Two modes of measurement exist  (Manweiler & Mull, 2017) : the Time of Flight (ToF) data and the energy-only A. Brunet et al. : J. Space Weather Space Clim. 2021, 11, 55  data (ISRHELT). As noted in the RBSPICE data user manual, the ISRHELT mode cannot separate the different ion species, but we assume that the protons are dominant in this energy range throughout the radiation belt. Thus, two datasets are available from the same instrument. The energy channels are the same for each dataset and each of the two spacecraft (RBSP-A and RBSP-B).
ISRHELT dataset As for almost all experimental data, there are several kinds of problems in RBSPICE ISRHELT data, such as contamination and bad data points. A deep analysis of these data shows that bad measurements appear during two time periods in the two first energy channels (41 keV and 46 keV): from 16/09/2014 to 20/09/2014 and 20/06/2017 to 23/06/2017 and in all energy channels of ISRHELT data before 22/02/2013. These data have been removed from the dataset. According to the PIs of the instrument (private discussion), the two first channels are close to the detector threshold and the noise level in the solid-state detectors (SSD) varies with RBSPICE temperature. The RBSPICE temperature was not closely controlled, and so these channels should not be used. Then, the data analysis shows that measurements at low L* values (L* being the third adiabatic invariant associated with the drift motion of the particles) are contaminated by very energetic protons in almost all energy channels.
ToF dataset The RBSPICE ToF measurements are good quality data, with none of the above-mentioned problems. However, at energy greater than 1 MeV, we can observe that proton fluxes measured by RBSPICE in this mode are very high during some periods (in 2015 and at the end of 2017) compared to those observed in ISRHELT data. Figure  5  shows an example of these differences for 5 MeV protons with an increase of the flux between L* = 3 and L* = 4 more important in the ToF data than in the ISRHELT data. The enhancement structures at these L* values are somewhat visible in both datasets but are really more accentuated in the ToF data. As presented in Figure  5 , NPOES-15/SEM2 does not observe such structures at nearly the same energy. It is important to remember that RBSP is nearly equatorial satellites while the NOAA POES constellation is in LEO.
However, according to the long duration of the structures seen in ToF datasets, the flux increase would be seen at LEO and near the equator. Figure  5  also shows the proton flux at higher energy (18 MeV) from RBSP-B/REPT, where the structures are not seen either (lower energies are not available on REPT). After discussion with the PIs on RBSPICE, instrument (private discussion), since we do not know that there are only protons in the energy channels greater than 1 MeV and because helium has a much higher efficiency for generating a TOF than protons do at those energies, there could be some helium in the observed rates. Consequently, in the scope of this study, we chose to prefer ISRHELT data for energies greater than 1 MeV than ToF data.
RBSPICE data used in the model Now, it is essential to obtain the best dataset using the two datasets from RBSPICE measurements. According to the analysis and the cleaning of these datasets described above, it is clear that the data used in the radiation model development should be a combination of the two datasets, neither of which is perfect. We know that some channels of ToF data are strange at high energies, and some channels of ISRHELT data are strange at low energies. Consequently, we will construct a dataset containing ToF data at low energies (<1 MeV) and ISRHELT data at high energies (>1 MeV). This combined RBSPICE dataset is presented versus L* and energy in Figure  6 , in the case of the year 2016.
Salammbosimulation results As in-flight data provide only partial coverage in time, space and energy, we have used a physics-based model to compute a complete covariance matrix with appropriate statistics. For this, we have used the Salammbô proton radiation belt model  (Beutier et al. , 1995; Maget et al. , 2008). This is a 3D (Energy, Pitch-angle, L* parameter) physics-based proton radiation belt -An empirical radial diffusion model, driven by the Kp geomagnetic index, as described in  Lejosne et al. (2013). -Nuclear interactions, charge exchange, and neutral collisions, based on the MSIS86 atmospheric model  (Hedin, 1987). -An empirical external boundary model at high L* derived from NOAA POES data, as described further down. The external boundary condition at L* value of 8 is defined as a Kappa distribution, with the following parameters: f L Ã ¼8 Ec ð Þ ¼ f 0 1 þ Ec jT À1Àj : ð1Þ This boundary condition is applied for energies below 500 keV.
Above this energy, the SEP flux measured by the NOAA GOES satellites are used. It is assumed that these geostationary satellites are always above the trapping boundary at these energies and that the flux at a given energy is constant across the different L* above this boundary  (Vacaresse et al. , 1999). The trapping boundary was fitted on CRRES data and is given by the following equation: L trap ¼ 6 À 0:282 Kp þ 3:5 Â 10 À3 Dst: ð2Þ For this model, we have simulated the period from 1989 to 2017, covering more than three solar cycles. Phase-Space Density (PSD) maps were produced twice per day on a relatively coarse grid (34 Â 25 Â 34 along the pitch angle, energy, and L* axes). From the obtained PSD maps, we computed the Omnidirectional Differential Proton Fluxes (hereby described as FPDO as in the PRBEM standard) using trapezoid integration.
Because of the relatively coarse grid, we observe some discrepancies between the simulated fluxes and the RBSPICE observations at low L* values, with large gradients in the densities. To a lesser extent, we also observe discrepancies between the datasets near the low energy boundary of the Salammbô domain. To avoid biasing our model on these regions where Salammbô is expected to behave relatively poorly, we filtered out all points below L* = 2 and at energies below 40 keV.
Model grid As described in Section 3, the statistical analysis required to construct the OMEP-EOR model has been carried on independently for the RBSP and Salammbô datasets, and the results were merged to produce the model. To allow for the statistical computations and merging, we have defined a common Cartesian grid to mesh the (a eq ¼ arcsin ffiffiffiffi ffi Beq B q , Ec, L*) space, where a eq is the equatorial pitch angle, B and B eq are the local and equatorial magnetic field magnitudes, and Ec the particle energy. The grid used in our model is described in Table  1. We note that, for low L* and low equatorial pitch-angles values, the points are ill-defined, as they lay in the atmosphere or below. We use the pitch angle of locally bouncing particles to denote the magnetic latitude of the points on the field lines.
Spatial model The spatial model describes the distribution of the proton radiation belt global state. In this model, we assume that the 12 h sampling period used in our input datasets is small enough to model the instantaneous state of the belt. We model this state as a multivariate lognormal distribution that is fitted independently on the two input datasets. We have computed the median state at each grid point and the spatial covariance matrix (where each coefficient is the covariance of the flux between two grid points), using the base 10 logarithm of the fluxes. For each model, we have filtered out any mesh point where too few points were available (less than 500 samples for the RBSP dataset and less than 15 000 samples in the Salammbô dataset). We have also filtered out every point in the Salammbô dataset at L* less than 2 or energies lower than 40 keV, as explained in Section 2.
Temporal model To compute the distributions of average fluxes on arbitrary durations, we need to have a model of the temporal correlations of the dataset. We have used a simple Gaussian process  (Williams & Rasmussen, 2006)  at each grid point to account for these correlations. The Gaussian process model assumes that the distribution of two samples at the same point is normal and that its covariance only depends on the time interval between the two samples. A. Brunet et al. : J. Space Weather Space Clim. 2021, 11, 55  This covariance is given by the following square exponential kernel: K dt ð Þ ¼ r 2 exp À dt 2 2s 2 ð3Þ where r 2 is the variance of the underlying data and s the characteristic time at the given point. These two parameters were fitted on the data. Figure  9a  presents three examples of temporal covariances measured and fitted for three different energies  (61, 539, and 4.
We note that the AP8 MIN and MAX models yield very nearly identical results on these energies, so only the AP8 MIN results are presented here. The AP9/SPM model was run on version 1. 50. 001 in mean mode, in which we have computed all deciles. Moreover, we have computed estimation of the 4 MeV proton flux mission average from the THEMIS-SST data. We can compute the average flux on the trajectory for a given starting date using proton flux maps produced from these instruments. By varying the starting date on the RBSP period (2012-2019), we have produced a distribution on the flux, corresponding to the variation of the proton belt on this period. We note that, due to contamination of the data, we could not use the data below L* = 1. 9, so for these points of the trajectory, a null flux was assumed.
To estimate the impact of this filtering, we have computed the AP8 flux while using null fluxes for these data points, and the resulting average flux is only 1. 2% smaller than the AP8 flux without filtering. The resulting median and 90th percentile energy spectrum are presented in Figure  12. First, we notice that all model spectra are relatively close to each other, compared to the variability between the median and 90th percentiles for the OMEP-EOR and AP9 models. The AP8 model presents higher fluxes at low energies (below 1 MeV) than the OMEP-EOR and AP9 models, both for the median and 90th percentile values. On the contrary, the AP8 fluxes between 2 MeV and 10 MeV fall below the  The spread of the distributions of the SPM is greater than both AP9 and the OMEP-EOR model, which reflects the larger uncertainties in the datasets involved in the creation of the Plasma Model.
These results highlight the high climatological variability of the proton belt at a few MeV, as the AP8 and AP9 are using data from previous solar cycles, and the OMEP-EOR model, as well as the THEMIS-SST data, correspond to the most recent solar cycle, during which very intense average proton fluxes were observed at these energies, compared to those observed during previous solar cycles. We believe that these recent observations give a good idea of a worst-case proton environment for solar cell degradation and that the OMEP-EOR can be used for designing upcoming EOR missions. As part of future developments, we plan to refine the temporal model to include solar-cycle dependencies and use the methodology developed here to model the dynamics of other challenging parts of the radiation belts, such as the slot in the electron belts.
Acknowledgements. This work was supported by the  European Space Agency 's  ARTES program  as part of the activity on  Electric Orbit Raising Radiation Environment and Solar Array Degradation (ARTES ESA  contract No. 4000127957/19/NL/NR ). The authors would like to thanks OHB for the trajectory files used in this article. The RBSPICE instrument was supported by  JHU/APL  Subcontract No. 937836  to the  New Jersey Institute of Technology under NASA  Prime Contract No. NAS5-01072. The authors would like to thanks  Louis Lanzerotti  and  Don Mitchell  for their insight and comments on the RBSPICE data during the writing of this article. The editor thanks two anonymous reviewers for their assistance in evaluating this paper. The editor thanks two anonymous reviewers for their assistance in evaluating this paper.
Modelling the rare but high-impact Mediterranean Heavy Precipitation Events (HPEs) at climate scale remains a largely open scientific challenge. The issue is adressed here by running a 38-year-long continuous simulation of the CNRM-AROME Convection-Permitting Regional Climate Model (CP-RCM) at a 2. 5 km horizontal resolution and over a large pan-Alpine domain. First, the simulation is evaluated through a basic Eulerian statistical approach via a comparison with selected high spatial and temporal resolution observational datasets. Northwestern Mediterranean fall extreme precipitation is correctly represented by CNRM-AROME at a daily scale and even better at an hourly scale, in terms of location, intensity, frequency and interannual variability, despite an underestimation of daily and hourly highest intensities above 200 mm/day and 40 mm/h, respectively.
A comparison of the CP-RCM with its forcing convection-parameterised 12. 5 km Regional Climate Model (RCM) demonstrates a clear added value for the CP-RCM, confirming previous studies. Secondly, an object-oriented Lagrangian approach is proposed with the implementation of a precipitating system detection and tracking algorithm, applied to the model and the reference COMEPHORE precipitation dataset for twenty fall seasons. Using French Mediterranean HPEs as objects, CNRM-AROME's ability to represent the main characteristics of fall convective systems and tracks is highlighted in terms of number, intensity, area, duration, velocity and severity. Further, the model is able to simulate long-lasting and severe extreme fall events similar to observations. However, it fails to reproduce the precipitating systems and tracks with the highest intensities (maximum intensities above 40 mm/h) well, and the model's tendency to overestimate the cell size increases with intensity.
2020; Pichelli et al. 2020). Few studies have been conducted specifically for the fall HPEs in the Mediterranean region using CP-RCMs. In the first European multi-model CP-RCMs intercomparison  (Coppola et al. 2020b) , one case study focuses on a Mediterranean HPE referred to as HyMeX-IOP16. In  Berthou et al. (2020) , improvement in the representation of the daily fall extreme precipitation in CP-RCMs compared to RCMs is shown for a ten-year period and also through a detailed case study. For a ten-year period focusing on the Cevennes region, the southern part of the Massif-Central most affected by fall HPEs (cf. Fig. 1 ),  Fumière et al. (2020)  use the new French reference hourly and kilometric observational dataset COMEPHORE to demonstrate the added value of CNRM-AROME CP-RCM, compared to CNRM-ALADIN RCM, for daily and hourly precipitation.
Similarly, until now, studies have been limited to relatively short periods due to calculation limitations for the model's simulations and the limited availability of reliable high temporal and spatial resolution observational datasets. We now have a 38-year-long simulation of the new version of the CNRM-AROME CP-RCM with a 2. 5 km resolution over the pan-Alpine domain defined through the CORDEX FPS on Convection program  (Coppola et al. 2020b). The new French reference hourly and kilometric observational dataset COME-PHORE has recently been extended to 20 years. Our study takes advantage of these opportunities. Its main objectives are: and apply a precipitating system detection and tracking algorithm in order to evaluate whether the CP-RCM is able to reproduce the main characteristics (duration, area, intensity, severity) of the convective systems observed in COMEPHORE.
Section 2 presents the observational datasets, models, simulation setup and methods used in the study. Section 3 proposes standard climate statistics and a comparison between models and observations, focusing on extreme precipitation and interannual variability at daily and hourly time-scales. Section 4 presents the object-oriented approach applied both to CNRM-AROME and COMEPHORE, allowing comparison between the CP-RCM and observations for the main characteristics of the precipitating systems and trajectories. Discussion is provided in Sect. 5 and a conclusion is given in Sect. 6.
Observational precipitation datasets In our study, we need high-resolution and high-quality observational datasets for three main reasons: -we want to evaluate a high spatial and temporal resolution model simulation, i. e. kilometrics and hourly, correctly; -our evaluation study focuses on precipitation, a parameter particularly difficult to estimate because of its significant variability in space and in time; -we are dealing with extreme rainfall, meaning the tail of the rainfall distribution, which is often poorly represented in observed datasets. Particular attention must therefore be paid to the choice of reference precipitation observed datasets  (Zolina et al. 2014; Prein and Gobiet 2017; Fantini et al. 2018; Kotlarski et al. 2019). The selected hourly and daily precipitation gridded datasets are described in Table  1.