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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Dynamical ejecta from binary neutron star mergers: Impact of a small residual eccentricity and of the equation of state implementation

Predicting the properties of the matter ejected during and after a neutron star merger is crucial to our ability to use electromagnetic observations of these mergers to constrain the masses of the neutron stars, the equation of state of dense matter, and the role of neutron star mergers in the enrichment of the Universe in heavy elements. Furthermore, our ability to reliably provide such predictions is however limited by a broad range of factors, including the finite resolution of numerical simulations, their treatment of magnetic fields, neutrinos, and neutrino-matter interactions, and the approximate modeling of the equation of state of dense matter. In this manuscript, we study specifically the role that a small residual eccentricity and different implementations of the same equation of state have on the matter ejected during the merger of a 1.3M ⊙ –1.4M ⊙ binary neutron star system. We find that a residual eccentricity e ~ 0.01, as measured ~ 4–6 orbits before merger, causes O(25%–30%) changes in the amount of ejected mass, mainly due to changes in the amount of matter ejected as a result of core bounces during merger. We note that O(1%) residual eccentricities have regularly been used in binary neutron star merger simulations as proxy for circular binaries, potentially creating an additional source of error in predictions for the mass of the dynamical ejecta.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

An Approach to Dependence Assessment in Human Reliability Analysis: Application of Lag and Linger Effects

Dependence assessment refers to an approach used in human reliability analysis (HRA) to adjust a human error probability (HEP) for the following action by considering the impact of the preceding action. It has been known to significantly affect the overall results of probabilistic safety assessment (PSA). If the dependence assessment is not adequate, the result could be unconvincing for explaining the operator failures in the context of PSA. To date, several methods and some recent research have identified suggestions for treating dependence issues in HRA; however, these are still exclusively based on the intrinsic approach of the Technique for Human Error Rate Prediction (THERP), an HRA method. THERP inevitably has a challenge with the subjectivity of expert evaluation as well as the requirement for PSA and HRA expertise with resource-intensive and time-consuming processes. This paper suggests an approach to dependence assessment that could not only minimize the influence of expert judgment, but also saves time to perform the analysis with reasonable manpower. It modifies existing HRA methods with considering lag and linger effects to apply dependence effects for them. Based on a representative HRA method, i.e., Standardized Plant Analysis Risk - HRA (SPAR-H), guidance for how to apply lag and linger effects for the HRA method is suggested. Then, an investigation is carried out to compare quantification results of the revised HRA method with that of the original approach based on experimental data.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Resilience and economics of microgrids with PV, battery storage, and networked diesel generators

Current designs and assessments of microgrids have ignored component reliability, leading to significant errors in predicting a microgrid’s performance while islanded. Existing life cycle cost studies on hybrid microgrids—which combine photovoltaics (PV), battery storage and networked emergency diesel generators—also have not identified all the potential economic opportunities. Reducing the number of emergency diesel generators through reliance on PV and battery, retail bill savings, and demand response and wholesale market revenue streams are all important. This paper provides a new statistical methodology that calculates the impact of distributed energy reliability and variability on a microgrid’s performance and a novel use of the optimization platform REopt to explore multiple cost savings and revenue streams. We examine the impacts for microgrids in California, Maryland, and New Mexico and show that a hybrid microgrid is a more resilient and cost-effective solution than a diesel-only system. Under realistic conditions, a hybrid microgrid can provide higher system reliability when islanded and have a lower life cycle cost under multiple market conditions than a traditional diesel generator-based system. The improved performance of the hybrid system is resilient to conditions experienced over the last 20 years in solar irradiance and sees little degradation in performance immediately after a hurricane. The cost savings to provide this more resilient backup power system as compared to a diesel-only microgrid are significant. The net present cost for a hybrid microgrid is 19% lower in New Mexico and 35% lower in Maryland than a diesel-only microgrid. In California, the net present cost of the hybrid microgrid is negative because, unlike a diesel-only microgrid, a hybrid microgrid has lower life cycle costs than the power costs without a microgrid.

25 ENERGY STORAGE↗
DOE OSTI2020

Comparison of active interrogation methods for source location in a scattering and absorbing medium, consisting of PGNAA, and an AmBe quasi-forward biased directional source

Source location of Special Nuclear Material (SNM) encompassing 95% 235 U and 239 Pu is identified by utilizing a directional source from Patent No: US20190013109A1 using Prompt Gamma Neutron Activation Analysis (PGNAA) and neutron spectroscopy simulated with Monte-Carlo N-Particle transport 6.2 (MCNP). BC-408, HPGe, LaBr 3 detector arrays were used to identify the location of the SNM using total counts incident on each detector, and PGNAA photopeaks from HPGe and LaBr 3 detector arrays in a polyethylene shield. The conducted simulations varied the volume and location of the SNM in the MCNP input files to observe how the source location method behaved. PGNAA photopeaks used for source identification include 61 keV from fission, 2.223 MeV prompt gamma from hydrogen, 511 keV annihilation, and a single and double escape peaks from the prompt gamma interaction from hydrogen. The capabilities of each detector systems to acquire well resolved photopeaks with a 1% relative error or less, and total relative error for F4 and F8 tallies were less than 0.015% relative error. Source predictions of the SNM with uneven amounts of polyethylene shielding between the source and detectors was observed to overpredict and give invalid source location predictions. Source locations of the SNM with even amounts of polyethylene material between the source and each detector were found to be valid. With a 1 Ci 241 Am source activity, it was determined that 1630 s were needed to obtain the results for each detector system with the quasi-forward directional AmBe source. Coupling source and material identification together would increase acquisition time but would only require one system to determine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Quantification of manganese for ChemCam Mars and laboratory spectra using a multivariate model

In this work, we report a new calibration model for manganese using the laser-induced breakdown spectroscopy instrument that is part of the ChemCam instrument suite onboard the NASA Curiosity rover. The model has been trained using an expanded set of 523 manganese-bearing rock, mineral, metal ore, and synthetic standards. The optimal calibration model uses the Partial Least Squares (PLS) and Least Absolute Shrinkage and Selection Operator (LASSO) multivariate techniques, with a novel “double blending” technique. We determined the detection limit for manganese is 82 ppm using a method blank procedure and is possibly as low as 27 ppm based on visual inspection of the spectra. Based on a representative test set consisting of measurements on 93 standards, the double blended multivariate model shows a Root Mean Squared Error of Prediction (RMSEP) accuracy of 1.39 wt% MnO for the full blended model. Employing a local RMSEP estimate where the model performance is evaluated based on nearby test samples, the accuracy is 0.03 wt% at the quantification limit (0.05 wt% MnO), 0.4 wt% accuracy at 1.0 wt% MnO, and 4.4 wt% accuracy at 100 wt% MnO. Precision is estimated using the standard deviation of the test set measurements, and is ±0.01 wt% MnO at the quantification limit, ±0.09 wt% MnO at 1.0 wt% MnO, and ± 2.1 wt% MnO at 100 wt% MnO (all 1 standard deviation). This new calibration is important for understanding the variation of manganese in the bedrock with the Curiosity rover on Mars, which provides insight into past redox conditions on Mars.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Post-landing major element quantification using SuperCam laser induced breakdown spectroscopy

The SuperCam instrument on the Perseverance Mars 2020 rover uses a pulsed 1064 nm laser to ablate targets at a distance and conduct laser induced breakdown spectroscopy (LIBS) by analyzing the light from the resulting plasma. SuperCam LIBS spectra are preprocessed to remove ambient light, noise, and the continuum signal present in LIBS observations. Prior to quantification, spectra are masked to remove noisier spectrometer regions and spectra are normalized to minimize signal fluctuations and effects of target distance. In some cases, the spectra are also standardized or binned prior to quantification. To determine quantitative elemental compositions of diverse geologic materials at Jezero crater, Mars, we use a suite of 1198 laboratory spectra of 334 well-characterized reference samples. The samples were selected to span a wide range of compositions and include typical silicate rocks, pure minerals (e.g., silicates, sulfates, carbonates, oxides), more unusual compositions (e.g., Mn ore and sodalite), and replicates of the sintered SuperCam calibration targets (SCCTs) onboard the rover. For each major element (SiO 2 , TiO 2 , Al 2 O 3 , FeO T , MgO, CaO, Na 2 O, K 2 O), the database was subdivided into five “folds” with similar distributions of the element of interest. One fold was held out as an independent test set, and the remaining four folds were used to optimize multivariate regression models relating the spectrum to the composition. We considered a variety of models, and selected several for further investigation for each element, based primarily on the root mean squared error of prediction (RMSEP) on the test set, when analyzed at 3 m. In cases with several models of comparable performance at 3 m, we incorporated the SCCT performance at different distances to choose the preferred model. Shortly after landing on Mars and collecting initial spectra of geologic targets, we selected one model per element. Subsequently, with additional data from geologic targets, some models were revised to ensure results that are more consistent with geochemical constraints. The calibration discussed here is a snapshot of an ongoing effort to deliver the most accurate chemical compositions with SuperCam LIBS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Leveraging visible and near-infrared spectroelectrochemistry to calibrate a robust model for Vanadium(IV/V) in varying nitric acid and temperature levels

Spectroelectrochemistry and optimal design of experiments can be used to rapidly build accurate models for species quantification and enable a greater level of process awareness. Optical spectroscopy can provide vital elemental and molecular information, but several hurdles must be overcome before it can become a widely adopted analytical method for remote analysis in the nuclear field. Analytes with varying oxidation state, acid concentration, and fluctuating temperature must be efficiently accounted for to minimize time and resources in restrictive hot cell environments. The classic one-factor-at-a-time approach is not suitable for frequent calibration/maintenance operations in this setting. Therefore, a novel alternative was developed to characterize a system containing vanadium(IV/V) (0.01–0.1 M), nitric acid (0.1–4 M), and varying temperatures (20–45 °C). Here, spectroelectrochemistry methods were used to acquire a sample set selected by optimal design of experiments. This new approach allows for the accurate analysis of vanadium and HNO 3 concentration by leveraging UV–Vis–NIR absorption spectroscopy with robust and accurate chemometric models. The top model's root mean squared error of prediction percent values were 3.47%, 4.06%, 3.40%, and 10.9% for V(IV), V(V), HNO 3 , and temperature, respectively. These models, efficiently developed using the designed approach, exhibited strong predictive accuracy for vanadium and acid with varying oxidation states and temperature using only spectrophotometry, which advances current technology for real-world hot cell applications. Additionally, Nernstian analysis of the V(IV/V) standard potential was performed using traditional absorbance methods and multivariate curve resolution (MCR). The successful tests demonstrated that MCR Nernst tests may be valuable in highly convoluted spectral systems to better understand the redox processes' behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Benchmarking magnetised three-wave coupling for laser backscattering: analytic solutions and kinetic simulations

Understanding magnetised laser–plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. For nanosecond pulses at non-relativistic intensities, interactions are dominated by coherent three-wave interactions, whose nonlinear coupling coefficients became known only recently when waves propagate at oblique angles with the magnetic field. In this paper, backscattering coupling coefficients predicted by warm-fluid theory are benchmarked using particle-in-cell simulations in one spatial dimension, and excellent agreements are found for a wide range of plasma temperatures, magnetic field strengths and laser propagation angles, when the interactions are mediated by electron-dominant hybrid waves. Systematic comparisons between theory and simulations are made possible by a rigorous protocol. On the theory side, the initial boundary value problem of linearised three-wave equations is solved, and the transient-time solutions allow the effects of growth and damping to be distinguished. On the simulation side, parameters are carefully chosen and calibration runs are performed to ensure that comparisons are well controlled. Fitting simulation data to analytical solutions yields numerical growth rates that match theory predictions within error bars. Although warm-fluid theory is found to be valid for a wide parameter range, genuine kinetic effects have also been observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

ARC physics basis–magnetohydrodynamics

ARC is designed to produce 400 ⁢MW of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the 𝑚/𝑛 =2/1 and 3/2 surfaces (with poloidal mode number 𝑚, and toroidal mode number 𝑛) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below 0.1% of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the 𝑛 =1 error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting 𝑛 =2 error fields to some degree and creating strong enough 𝑛 =2 or 𝑛 =3 edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Comparing Sensor Fusion and Multimodal Chemometric Models for Monitoring U(VI) in Complex Environments Representative of Irradiated Nuclear Fuel

Optical sensors and chemometric models were leveraged for the quantification of uranium(VI) (0–100 μg mL –1 ), europium (0–150 μg mL –1 ), samarium (0–250 μg mL –1 ), praseodymium (0–350 μg mL –1 ), neodymium (0–1000 μg mL –1 ), and HNO 3 (2–4 M) with varying corrosion product (iron, nickel, and chromium) levels using laser fluorescence, Raman scattering, and ultraviolet–visible–near-infrared absorption spectra. In this paper, an efficient approach to developing and evaluating tens of thousands of partial least-squares regression (PLSR) models, built from fused optical spectra or multimodal acquisitions, is discussed. Each PLSR model was optimized with unique preprocessing combinations, and features were selected using genetic algorithm filters. The 7-factor D-optimal design training set contained just 55 samples to minimize the number of samples. The performance of PLSR models was evaluated by using an automated latent variable selection script. PLS1 regression models tailored to each species outperformed a global PLS2 model. PLS1 models built using fused spectra data and a multimodal (i.e., analyzed separately) approach yielded similar information, resulting in percent root-mean-square error of prediction values of 0.9–5.7% for the seven factors. Further, the optical techniques and data processing strategies established in this study allow for the direct analysis of numerous species without measuring luminescence lifetimes or relying on a standard addition approach, making it optimal for near-real-time, in situ measurements. Nuclear reactor modeling helped bound training set conditions and identified elemental ratios of lanthanide fission products to characterize the burnup of irradiated nuclear fuel. Leveraging fluorescence, spectrophotometry, experimental design, and chemometrics can enable the remote quantification and characterization of complex systems with numerous species, monitor system performance, help identify the source of materials, and enable rapid high-throughput experiments in a variety of industrial processes and fundamental studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Simultaneous quantification of uranium( VI ), samarium, nitric acid, and temperature with combined ensemble learning, laser fluorescence, and Raman scattering for real-time monitoring

In this work, laser-induced fluorescence spectroscopy (LIFS), Raman spectroscopy, and a stacked regression ensemble was developed for near real-time quantification of uranium(VI) (1–100 μg mL –1 ), samarium (0–200 μg mL –1 ) and nitric acid (0.1–4 M) with varying temperature (20 °C–45 °C). LIFS applications range from fundamental lab-scale studies to real-time process monitoring at industrial levels, such as nuclear reprocessing applications, provided the phenomena affecting the fluorescence spectrum are accounted for (e.g., absorption, quenching, complexation). Multiple chemometric models were examined and compared to a more traditional multivariate regression approach called partial least squares (PLS). Results obtained on synthetic samples selected using D-optimal experimental design indicated that a stacked regression method, which included ridge regression, random forest, PLS, and an eXtreme gradient boost algorithm, successfully measured uranium(VI) concentrations directly in nitric acid without measuring luminescence lifetimes or standard addition. The top model resulted in percent root-mean-square error of prediction values of 5.2, 1.9, 3.0, and 2.3% for U(VI), Sm 3+ , HNO 3 , and temperature, respectively. The approach may be useful for quantifying fluorescent fission products (e.g., Sm 3+ ) to provide information on burnup of irradiated nuclear fuel. This novel framework reinforces the applicability of LIFS for real-time applications in nuclear fuel cycle applications.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Online monitoring of lanthanide species with combined spectroscopy in flowing aqueous aerosol systems

Combined spectroscopic analysis through absorption and laser-induced breakdown spectroscopy (LIBS) was used to monitor Nd and Pr concentrations in a flowing aqueous system. A unique, online sampling approach was employed that allowed for an approximately closed analysis loop of liquids from a reservoir. Absorption spectroscopy was performed with an optical flow cell, and LIBS was performed on an aerosol stream. Multivariate calibrations based on combined absorption and LIBS signals were built for Nd and Pr and then used to monitor concentrations in mixed solutions in a series of spiking tests. In these tests, the concentrations of Nd and Pr in solution were intermittently changed while spectroscopic signals were monitored in real-time. The combined spectroscopic signals and multivariate models were successful in monitoring changing concentrations of lanthanide species with high accuracy and minimal latency. Root-mean squared error of predictions were 0.015 mol L −1 and 0.019 mol L −1 for Nd and Pr respectively, and these lanthanides were able to be monitored to an accuracy of < 0.2 wt%. This work demonstrates both the capabilities of a sampling system for online analysis of liquids and the capabilities of multimodal spectroscopic characterization for real-time, continuous tracking of species in potentially hazardous liquid systems.

absorbance spectroscopy↗
DOE OSTI2020

Examining the order-of-limits problem and lattice constant performance of the Tao–Mo functional

In their recent communication a semi-local density functional derived from the density matrix expansion of the exchange hole localised by a general coordinate transformation. We show that the order-of-limits problem present in the functional, dismissed as harmless in the original publication, causes severe errors in predicted phase transition pressures. We also show that the claim that lattice volume prediction accuracy exceeds that of existing similar functionals was based on comparison to reference data that misses anharmonic zero-point expansion and consequently overestimates accuracy. Here, by highlighting these omissions, we give a more accurate assessment of the Tao-Mo functional and show a possible direction for resolving the order-of-limits problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Extraction of mechanical properties of materials through deep learning from instrumented indentation

Instrumented indentation has been developed and widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials. This method is particularly desirable for those applications where it is difficult to experimentally determine the mechanical properties using stress–strain data obtained from coupon specimens. Such applications include material processing and manufacturing of small and large engineering components and structures involving the following: three-dimensional (3D) printing, thin-film and multilayered structures, and integrated manufacturing of materials for coupled mechanical and functional properties. Here, we utilize the latest developments in neural networks, including a multifidelity approach whereby deep-learning algorithms are trained to extract elastoplastic properties of metals and alloys from instrumented indentation results using multiple datasets for desired levels of improved accuracy. We have established algorithms for solving inverse problems by recourse to single, dual, and multiple indentation and demonstrate that these algorithms significantly outperform traditional brute force computations and function-fitting methods. Moreover, we present several multifidelity approaches specifically for solving the inverse indentation problem which 1) significantly reduce the number of high-fidelity datasets required to achieve a given level of accuracy, 2) utilize known physical and scaling laws to improve training efficiency and accuracy, and 3) integrate simulation and experimental data for training disparate datasets to learn and minimize systematic errors. The predictive capabilities and advantages of these multifidelity methods have been assessed by direct comparisons with experimental results for indentation for different commercial alloys, including two wrought aluminum alloys and several 3D printed titanium alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The impact of new d(p,γ)3 rates on Big Bang Nucleosynthesis

We consider the effect on Big Bang Nucleosynthesis (BBN) of new measurements of the d(p,γ) 3 He cross section by the LUNA Collaboration. These have an important effect on the primordial abundance of D/H which is also sensitive to the baryon density at the time of BBN. We have re-evaluated the thermal rate for this reaction, using a world average of cross section data, which we describe with model-independent polynomials; our results are in good agreement with a similar analysis by LUNA. We then perform a full likelihood analysis combining BBN and Planck cosmic microwave background (CMB) likelihood chains using the new rate combined with previous measurements and compare with the results using previous rates. Concordance between BBN and CMB measurements of the anisotropy spectrum using the old rates was excellent. The predicted deuterium abundance at the Planck value of the baryon density was (D/H) BBN+CMB old = (2.57 ± 0.13) × 10 –5 which can be compared with the value determined from quasar absorption systems (D/H) obs = (2.55 ± 0.03) × 10 –5 . Using the new rates we find (D/H) BBN+CMB = (2.51 ± 0.11) × 10 –5 . We thus find consistency among BBN theory, deuterium and 4He observations, and the CMB, when using reaction rates fit in our data-driven approach. We also find that the new reaction data tightens the constraints on the number of relativistic degrees of freedom during BBN, giving the effective number of light neutrino species N ν = 2.880 ± 0.144 in good agreement with the Standard Model of particle physics. Lastly, we note that the observed deuterium abundance continues to be more precise than the BBN+CMB prediction, whose error budget is now dominated by d(d,n) 3 He and d(d,p) 3 H.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Disentanglement of density and rotation dependences of the field penetration threshold on the J-TEXT tokamak

The field penetration threshold of magnetic perturbations has been observed to vary non-monotonically with an increase of density in ohmic plasmas on the J-TEXT tokamak. This observation appears contradicting the previous empirical density scaling law. Disentanglement of plasma density and rotation dependences of the field penetration threshold has been carried out. It shows that the field penetration threshold depends only weakly on the density but linearly on the plasma rotation. This result is not only important for the prediction of error field tolerance in fusion devices, but also opens a question on the role of density in the forced magnetic reconnection process in magnetized plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Formulation of autoconversion and drop spectra shape in shallow cumulus clouds

Two-moment autoconversion parameterizations as compared to accretion parameterizations exhibit significant errors suggesting that additional moments are needed to increase their accuracy. We develop a three-moment autoconversion parameterization using output from an LES model with size-resolved microphysics. Adding the third moment decreases the errors of parameterization and improves precipitation prediction. However, the errors are still significantly larger than errors of accretion rate. An analysis of the cloud drop size distributions (DSDs) in the simulated tropical convective cloud system reveals that most of DSDs have a significant fraction of cloud liquid water content (qc) in the mid-size droplet range (radii from 20 to 40 microns). Our data indicates that more than 30% of DSDs have over half of qc contained in the mid-size range and about 60% of spectra have, at least, one third of qc in this range. Even when the rain/drizzle mode is small (radar reflectivity Z < -10 dBZ), there is a significant number of spectra in which fraction of qc in the mid-size range is as large as 60%. These DSDs are more complex than the frequently used single-mode Gamma or Log-normal distributions, which usually do not have a considerable tail extending to the mid-size range and can be defined by three microphysical moments. The need to define DSDs by more than three moments explains the large errors in the three-moment autoconversion parameterization. The limitation of three-parameter Gamma or Log-normal distributions should be kept in mind when applying them in precipitating shallow Cu clouds.

Kogan, Yefim↗