dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction The DarkSide program goal is to detect signals of dark matter (DM) particles, by using liquid argon (LAr) as a target in a dual-phase Time Projection Chamber (TPC) with active background suppression systems. In order to achieve the goal, various technologies are adopted to reduce and reject background events. The main motivation to use LAr is its strong pulse shape discrimination (PSD) of electron recoils (ERs) from nuclear recoils (NRs). Considering that the dominant mechanism to detect an interaction between heavy DM (>10GeV/c 2 ) and baryonic matter is expected to be elastic scattering off nuclei, PSD in LAr provides a tool to reject the dominant background of ERs. The results from DarkSide-50 with atmospheric argon (AAr) data show that using PSD, a total of 1. 5×10 7 ER events can be completely rejected in the DM energy region of interest (ROI), leaving no events after an exposure of (1422±67)kg day  [1].
Dark Matter Search with an Underground Ar Target The underground argon (UAr) was extracted from a stream of gas from a CO 2 well in Cortez, Colorado, which also contained other gases including N 2 and He. Most of the CO 2 and N 2 was removed on site and a mixture of ∼5% Ar, ∼5% N 2 , and 90% He was sent to Fermilab for purification by cryogenic distillation  [3]. DarkSide-50 TPC was filled with the purified UAr at LNGS in Italy on April 1, 2015. To determine the 39 Ar depletion factor, the UAr data was compared to a GEANT4-based MC simulation. The MC was tuned on high statistic AAr data and validated against several γ calibration sources. The 39 Ar and 85 Kr activities were measured from a simultaneous fit of the MC to S1 data taken with the field off (See Fig. 1 ) and field-on (200 V/cm) data.
Mass-dimensional relationships (m 2 D) have been published for decades to characterize the microphysical properties of ice cloud particles. Classical m 2 D retrieval methods employ a simplifying assumption that restricts the form of the mass-dimensional relationship to a power law, an assumption that was proved inaccurate in recent studies. In this paper, a nonstandard approach that leverages optimal use of in situ measurements to remove the power-law constraint is presented. A model formulated as a linear system of equations relating ice particle mass to particle size distribution (PSD) and ice water content (IWC) is established, and the mass retrieval process consists of solving the inverse problem with numerical optimization algorithms. First, the method is applied to a synthetic crystal dataset in order to validate the selected algorithms and to tune the regularization strategy.
Subsequently, the method is applied to in situ measurements collected during the High Altitude Ice Crystal-High Ice Water Content field campaigns. Preliminary results confirm the method is efficient at retrieving size-dependent masses from real data despite a significant amount of noise: the IWC values calculated from the retrieved masses are in good agreement with reference IWC measurements (errors on the order of 10%-15%). The possibility to retrieve ice particle size-dependent masses combined with the flexibility left for sorting datasets as a function of parameters such as cloud temperature, cloud type, or convective index makes this approach well suited for studying ice cloud microphysical properties.
1) EARLY STUDIES ON ICE CRYSTALS: COLLECTION ON GROUND Early studies related to natural ice crystal mass focused on solid precipitating particles collected on ground  (Nakaya and Terada 1935; Zikmunda and Vali 1972; Kajikawa 1972; Locatelli and Hobbs 1974; and more recently Mitchell et al. 1990, among others). In these studies, ice particles ranging from hundreds of micrometers to several millimeters in size were collected, photographed, and classified into habit categories. The individual crystal mass was estimated from the droplet produced by crystal melting, and habit-dependent m 2 D relationships were derived for each subset. The retrieval process consists of fitting the individual mass against size data points using linear regression tools in log-log space, which produces power-law-type m 2 D relationships, noted as m 5 aD b , where the prefactor a and the exponent b are constant values that are specific to each habit.
MASS-SIZE RELATIONSHIPS The use of aircraft in atmospheric research projects has given access to a large panel of cloud types, and with concomitant improvement of airborne instrumentation and data processing techniques, in situ measurement datasets have laid the groundwork for the study of natural ice cloud particles' microphysical properties. In the early days,  Heymsfield (1972)  applied the on-ground mass measurement principle on board a research aircraft in order to analyze natural crystals sampled in cirrus clouds. Since then, technical developments of optical array probes (OAPs), total water content (TWC) probes, and cloud radar have made ice crystal ensemble properties, such as particle size distribution (PSD), ice water content (IWC), and radar reflectivity (Z e ), readily accessible.
While these two dynamical retrieval methods may capture the natural variability in ice particle ensembles along the flight path (e. g. , the change in particle morphology, dominant habits, density), they both implicitly assume that the dependence of mass on size conforms to a single power law irrespective of the particle size. Furthermore, they produce as many (a, b) pairs as there are points in the dataset, which might be impractical for use in models unless reduced to a single averaged m 2 D. As plots in log-log space of relationships found in literature show evidence that m 2 D is not linear over a broad size range,  Erfani and Mitchell (2016)  recently argue that a single m 2 D power law cannot satisfactorily represent the variation of mass over the size range spanned by atmospheric ice particles.
(2012)  support these considerations, which suggest that accounting for the size dependence of particles' properties, such as crystal habit distribution, could improve the mass retrieval. The situation is even worse when only one (a, b) pair is derived from an entire dataset. In this case the m 2 D parameterization fails to capture the spatiotemporal variability in the microphysical properties of ice particles within clouds. Since earlier methods based on individual crystal mass measurements are impractical for use in large datasets of mixed-habit ice particles, there is still a strong need for the development of alternative concepts for m 2 D retrieval methods. This study presents a nonstandard approach that leverages the optimal use of common in situ measurementsnamely, PSD and IWC-to waive the power-law constraint and therefore better capture the dependence of particle microphysical properties on size.
Section 2 introduces the assumptions made to set up a simple forward model that relates particle-size-dependent mass to PSD and bulk IWC values, as well as the mathematical formalism and tools selected to retrieve the particles' mass by solving the inverse problem. The method is then applied to simulated crystal populations (section 3) and to real cloud in situ measurements extracted from the HAIC-HIWC dataset (section 4). In this article, the emphasis is placed on the problem statement and technical aspects of this new mass retrieval process rather than on the implications of the preliminary results presented in section 4 for modeling and remote sensing retrieval algorithms.
(i) Characteristic parameters Time invariance of the parameters is assumed for each 5-s average data point: all particles sampled during a 5-s time interval are characterized by the same parameters (e. g. , the time-averaged value computed from the 1-Hz original measurements). Subsequently, datasets can be sorted into subsets of consistent data points using these parameters as sorting criteria. In such a subset where the characteristic parameters are invariant, the mass depends only on volume. Equation (1) becomes M 5 M jP 1 ,. ,P n (V, P 1 ,. , P n ) 5 M(V). ( 2 ) (ii) Volume In the ith bin of the PSD, the variability in the particle's size, D eq , depends on the bin width w i. As w i is generally small, the variability in D eq is small. It is further postulated that the spread in volume is also reasonably low within a bin (discussed in more detail in section 3b).
This system of linear equations can be written as a matrix equation: PSD Á m 5 iwc, (5) where d PSD 2 R P3N is a matrix in which PSDs are vertically concatenated, d iwc 2 R P is a vector of P IWC values, and d m 5 (m 1 m 2. m N ) T is the vector of N unknown reference masses. Thus, the forward model is formulated as a matrix equation that relates in situ measurements to the unknown bin reference masses. It is worth mentioning that the model does not require prior knowledge of the descriptors P 1 , P 2 ,. , P n. Sensitivity studies in which reference masses are retrieved from two distinctive subsets will reveal whether the parameter that differentiates between the two subsets influences the mass of ice particles (see section 4 for an example with sampling temperature as a descriptor). , where s max and s min are the largest and smallest singular values of the PSD matrix, respectively-indicate that measurement uncertainties and noise inherent to the measured data significantly influence the solution: the problem written with synthetic data (case presented in section 3) is severely ill-conditioned (c.
10 4 ) and the problem using HAIC-HIWC real data (case presented in section 4) is ill-posed (c / '). To circumvent the difficulty related to numerical instabilities, we follow the regularization approach presented in  Idier (2008)  and search for a solution that minimizes a composite criterion, noted as J(m): J(m)5 def kPSD Á m 2 iwck 2 1 l Á R(m) , (6) where J(m) is twofold: d The first term is referred to as the least squares term. Minimizing that term forces the solution vector to fit the measurements and to satisfy Eq. (  5 ). d The second term, referred to as regularization term, allows the introduction of some prior information that the solution should fulfill in order to qualify from a physical point of view and helps in reducing the noise propagation on the solution. The retrieved solution will be a trade-off between fidelity to the measured data and compliance with prior information embedded in the regularization term.
d k 5 2$ 2 J(m (k) ) 21 Á =J(m (k) ). ( 10 ) The step length a k is computed either iteratively with a backtracking line search algorithm given in  Nocedal and Wright (2006)  (applied to the HAIC-HIWC dataset in section 4) or explicitly from Eq. (  11 ) (applied to synthetic data in section 3): a k 5 2 =J(m (k) ) T d k d T k $ 2 J(m (k) )d k. ( 11 ) The new iterate m (k11) is computed from Eq. (  9 ), and this calculation is repeated until convergence of the sequence fJ(m (k) )g k is reached, with « 5 2. 2204 3 10 216 as the stopping criterion. The regularization parameter l controls the degree of regularization applied to the problem. Several techniques are available to identify the optimal l, that is, the value yielding the best compromise between the two terms of the objective function.
a. Generation of the synthetic dataset The generation of a synthetic dataset starts with the simulation of ice particle models using an Interactive Data Language (IDL) program  (Fontaine 2014; Fontaine et al. 2014). A model is characterized by its shape and dimensional properties, which are defined in Fig. 1  and summarized in Table  1. Each model is randomly rotated in space and projected to produce a 2D image. This process reproduces the working principles of OAPs and how 2D images are produced from real 3D crystals. The rotation/projection step is repeated 100 times, such that 100 2D images are created from each 3D model. The images are then processed to derive D eq using the same image processing software as for OAP images. The resulting size interval of D eq available for each crystal habit is indicated in the last column of Table  1.
PSD bins are then populated by randomly picking up crystals based on their D eq from habit tables with respect to the number and habits prescribed by the user's input. For each bin the theoretical bin reference mass, m ref ,i for the i th bin, is calculated as the average of the theoretical masses of the binned particles. This value is stored for later comparison with the bin reference mass retrieved by solving the inverse problem. IWC th is calculated by summing the actual mass of all the elements in the population. Finally, a synthetic dataset is composed of P different data points that are generated by randomly varying m (m 0 # m # m 0 1 100) and s (100 # s # 200). To test the retrieval method, three synthetic datasets are used: d One optimization dataset, noted as DS1: this is the dataset to which the optimization process is applied.
Twice as many PSDs as unknowns are generated (P 5 2N) to ensure that the PSD matrix in Eq. (  5 ) has a full rank. In DS1, m 0 5 300. The unknown mass vector m of Eq. (  5 ) (whose elements are the sought bin reference masses) is found by minimizing Eq. (  6 ) written with PSD DS1 and IWC th,DS1 quantities. d Two validation datasets, noted DS2 and DS3, are used to test the mass vector retrieved from DS1 on populations dominated by small (m 0 5 100 mm) and large (m 0 5 600 mm) particles, respectively. IWC values, noted IWC cal,DS2 and IWC cal,DS3 , are calculated from the retrieved mass vector m and PSD DS2 and PSD DS3 matrices, respectively. These calculated values are then compared to the corresponding IWC th for each data point. Furthermore, some statistical reference vectors can be defined, since the masses of all individual particles in the population are known: The mass retrieval process uses PSD as input data.
In addition to the unavoidable measurement uncertainties, approximations made in the forward model also make the PSD a noisy input for inversion. In the frame of the proposed inverse problem approach, the synthetic dataset is first used as an opportunity to study the noise contained in PSDs based on OAP images. The concept of bin reference mass relies on the assumption that PSD bins are natural subensembles where the crystals' mass is uniform, which in turn holds if: 1) PSD bins are narrow and 2) the size descriptor used to generate PSD accurately describes the particles' volume. These conditions are hardly met in reality. On the one hand, the width of a PSD size class is driven by the OAP specifications: it cannot be smaller than the probe resolution, which is nonnegligible (e. g. , 10-100 mm, as detailed later in section 4).
4 ). This habit mixture law applies to the three datasets (DS1-DS3). The results obtained for the first two test cases are not reported in the present article, but they helped in the definition of the regularization term and specifically in the choice of D elements: if masses of spherical ice particles of diameter equal to the bin center were selected as weighting coefficients in the regularization matrix for simplicity reasons, it was found by trial and error that adding the 15-mm offset to sphere diameters yielded improved estimates of the retrieved masses in small size bins, that would have been otherwise underestimated when particle habits significantly depart from spherical shape. The last test case is quite challenging because abrupt changes in crystal habits between two consecutive bins produce sharp variations of mass with size.
a. HAIC-HIWC dataset In the frame of HAIC-HIWC projects  (Dezitter et al. 2013; Strapp et al. 2016a) , two airborne field campaigns were held in Darwin, Australia, in 2014 and out of Cayenne, French Guyana, in 2015. With the overarching goal of characterizing ice particles in mesoscale convective systems (MCSs), these campaigns resulted in nearly 15 000 data points each, sampled at different stages of cloud life cycle in both oceanic and continental convection. This makes the HAIC-HIWC dataset one of the most comprehensive datasets on MCSs from the standpoint of the microphysical properties of hydrometeors. In this section we use data taken from three flights, as reported in Table  4. The optimization is conducted on the data of Darwin flight 16 (D16): all data points were sampled in the same oceanic MCS at a single temperature level (236.
1 K) such that the dataset is consistent with respect to two parameters (cloud temperature and cloud type) potentially influencing the particles' mass. The other reasons for choosing D16 as the optimization dataset is the high number of data points (1051 data points) and the large size range covered by the sampled particles. The validation is carried out on data from two arbitrarily chosen flights: d Cayenne flight 26 (C26) was performed one year later in coastal convection. Three temperature levels (264, 244. 2, and 229. 4 K) were sampled, and all data points (1298 in total) are conserved so that the potential effects of temperature on the retrieved particle mass can be assessed. The analysis considers only data points measured during level flight periods in areas where IWC values are larger than 0.
Since the particle's true masses are unknown, the quality of the mass retrieval is indirectly estimated by comparing the IWC values calculated from this mass vector to the reference IWC values measured by the IKP-2 instrument. A comparison between the calculated and measured IWC values is presented in Figs. 5c-e for the three datasets, and the quantitative results are summarized in Table  5. Unsurprisingly, the best agreement (IWC MAPE 5 10:5%) is found for D16, which supports the minimization process. The IWC prediction is equally satisfying for D19 (IWC MAPE 5 12:1%), where efforts have been made to sort data points into a coherent subset with respect to sampling temperature. Perhaps most interesting are the results of the IWC retrieval from C26 data. In Fig. 5c , points are color coded with temperature and three distinct groups are clearly visible (dark blue for the 229.
4 K in the C26 dataset (936 out of 1298; see Table  4 ). These results suggest that 1) ice particles observed in the D16, D19, and C26 MCSs at comparable temperature levels may have similar mass properties and 2) in the same cloud, particles sampled at different temperature levels may have different mass properties. Since the good agreement between calculated and measured IWC values observed for D19-244. 2 K and C26-229. 4 K may hide compensating errors, the next step will be to apply the method on subsets sampled at the same temperature level in different clouds and compare the retrieved quantities. Subsequently, the method will be applied to subsets sampled at different temperature levels in order to evaluate whether a first-order approximation model describing the mass of ice particles as a function of their size and the cloud temperature produces consistent results.
If not, we will expand the study to a multiparameter approach and search for potential correlations between the crystal mass and some other yet undefined parameters by applying the method to different subsets with specific environmental conditions. This, as well as any specific findings in ice particle microphysical properties and the implications for modeling and remote sensing retrieval algorithms, is well beyond the scope of this technical paper, which is focusing on the development of the technique and the numerical tool. Last but not least, the convergence of the optimization algorithms is reached after a very small number of iterations. Practically, the mass vector plotted in Fig. 5  is computed within few seconds on an ordinary computer. It underlines the efficiency of the present method in retrieving particle mass from large datasets of collocated and simultaneous PSD and IWC in situ measurements.
Conclusions and perspectives This article presents a new approach for the retrieval of ice particles' size-dependent masses from in situ measurements. A conceptual model is formulated as a linear system of equations relating particle mass to PSD and IWC measurements. The mass retrieval process consists of solving the inverse problem with numerical optimization tools. The strength of this technique is to make optimal use of common in situ measurements in order to waive the power-law assumption that is classically employed to constrain m 2 D relationships, although it has been proved inaccurate by recent studies. The new technique simplifies the computation of ice particle mass from large in situ measurement datasets and proves its worth when applied to aircraft data collected during HAIC-HIWC field campaigns: IWC values estimated from the retrieved particle masses match the measured values with 10%-15% accuracy.
The preliminary m 2 D test calculations reveal some interesting size-dependent features otherwise hindered by the power-law assumption. In future work, this data processing technique will be applied to process the whole HAIC-HIWC dataset with the overall objective to develop a statistical model of ice particle mass, taking into account temperature and any other relevant physical parameters (IWC value, cloud type, etc. ) susceptible to influence the mass of ice particles. The method is thought to be directly applicable to any collocated PSD and IWC measurement datasets, provided the number of available data points is compatible with the number of unknown elements of the mass vector to be solved. The authors believe such an approach could be adapted to retrieve ice particle mass from PSD and other bulk measurements, such as radar reflectivity factors, as long as an inverse problem can be formulated.
PSD shape: The size range considered in the synthetic test cases is (10 2 940) mm. Simulated crystals are sized into 93 equally spaced 10-mm-wide bins, and the number of particles per bin is prescribed by a normal probability density function of the bin midpoint multiplied by a prefactor so that there are approximately 10 000 elements in each population (or data point). The normal distribution parameters-namely, its mean m and standard deviation s-are changed from one data point to the other when generating the synthetic dataset, as detailed below.
Lower and upper bounds: vectors whose elements are the minimum and maximum theoretical bin reference masses, respectively, found across the dataset d Average bin reference mass [m th 5 (m th,1 m th,2. m th,N )]: vector whose elements are the average of the theoretical bin reference mass (m ref,i ) calculated over the dataset Some quantitative criteria are calculated to estimate the quality of retrieved values: d Mass percent error (PE) is computed for each bin from the retrieved mass value (m i , optimization output) and m th,i : PE i (%) 5 100 m i 2 m th,i the number of bins in the PSD, indicates the accuracy of the mass retrieval process d IWC mean absolute percentage error: IWC MAPE(%) 5 100 P å P i51 jIWC cal;i 2 IWC th;i j IWC th;i , where P is the number of data points in the set, indicates the accuracy of the IWC retrieval process b.
Acknowledgments. The research leading to these results received funding from (i) the  European Union 's  Seventh Framework Programme  in research, technological development, and demonstration under Grant Agreement  ACP2- GA-2012-314314 ; (ii) the  European Aviation Safety Agency (EASA)  Research Program under Service Contract EASA. 2013. FC27; and (iii) the  Federal Aviation Administration (FAA) ,  Aviation Research Division and Aviation Weather Division , under Agreement  CON-I-1301  with the  Centre National de la Recherche Scientifique. Funding to support the  Darwin  flight project was also provided by the  NASA   Aviation Safety Program , the  Boeing Co. , and  Transport Canada. Additional support was also provided by  Airbus Operations SAS, Science Engineering Associates , the  Bureau of Meteorology, Environment Canada (now Environment and Climate Change Canada ), the  National Research Council of Canada , the  University of Utah , and the  National Science Foundation  under Grant  AGS 12-13311.