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At least 91 records · Page 5

Evaluation of the Effect of Surface Finish on High-Cycle Fatigue for SLM-IN718

A high-cycle fatigue (HCF) knockdown factor was estimated for Inconel 718, manufactured with the selective laser melt (SLM) process. This factor is the reduction at a common fatigue life from the maximum stress in fatigue for low-stress ground (LSG) specimens to the maximum stress of those left with the original surface condition. Various vendors provided specimens. To reduce the number of degrees-of-freedom, only one heat treat condition was evaluated. Testing temperatures included room temperature, 800F, 1000F, and 1200F. The two surface conditions were compared at constant lives, where data was available. The recommended knockdown factor of the as-built surface condition (average roughness of approximately 245 micro-inches/inch) versus low-stress ground condition (roughness <= 4 micro-inches/inch) is approximately 1/3 or 33%. This is to say that for the as-built surface condition, a maximum stress of 2/3 of the stress for LSG can be expected to produce the same life in the as built surface condition. As an alternative method, the surface finish was incorporated into a new parameter with the maximum stress. The new parameter was formulated to be similar to the fracture mechanics stress intensity factor, and it was named the pseudo stress intensity factor, Kp. Using Kp, the variance seemed acceptable across all sources, and the knockdown factor was estimated over the range of data identified by Kp where data occurred. A plot of the results suggests that the knockdown factor is a function of temperature, and that for low lives the knockdown is greater than the knockdown observed above about one million cycles, where it stabilizes. One data point at room temperature was clearly different, and the sparsity of data in the higher life region reduces the value of these results. The method does appear to provide useful results, and further characterization of the method is suggested.

Lambert, Dennis M.↗

New methods to improve the vertical extrapolation of near-surface offshore wind speeds

Accurate characterization of the offshore wind resource has been hindered by a sparsity of wind speed observations that span offshore wind turbine rotor-swept heights. Although public availability of floating lidar data is increasing, most offshore wind speed observations continue to come from buoy-based and satellite-based near-surface measurements. The aim of this study is to develop and validate novel vertical extrapolation methods that can accurately estimate wind speed time series across rotor-swept heights using these near-surface measurements. We contrast the conventional logarithmic profile against three novel approaches: a logarithmic profile with a long-term stability correction, a single-column model, and a machine-learning model. These models are developed and validated using 1 year of observations from two floating lidars deployed in US Atlantic offshore wind energy areas. We find that the machine-learning model significantly outperforms all other models across all stability regimes, seasons, and times of day. Machine-learning model performance is considerably improved by including the air–sea temperature difference, which provides some accounting for offshore atmospheric stability. Finally, we find no degradation in machine-learning model performance when tested 83 km from its training location, suggesting promising future applications in extrapolating 10 m wind speeds from spatially resolved satellite-based wind atlases.

17 WIND ENERGY↗

Adaptive Pressure Profile Method to Locate the Isolator Shock Train Leading Edge Given Limited Pressure Information

To maximize the performance of high-speed air-breathing engines, such as dual-mode scramjets, the streamwise location of the shock train leading edge (STLE) is ideally placed as far upstream in the isolator as possible while avoiding engine unstart. Thus, it is of interest to quantify and control the STLE location as the vehicle travels along its flight trajectory. The STLE location is typically quantified using wall static pressure measurements but there are often restrictions on the number and placement of transducers, thus reducing the accuracy and overall capability of STLE detection methods. In this work, the Adaptive Pressure Profile (APP) method is introduced to address such sparsity concerns. This method is data driven and does not heavily rely on prior information about the flow regime or engine model. Instead, the \mname method uses real-time pressure measurements from a small number of transducers to adaptively learn the isolator pressure profile. This adaptively-learned profile is fit to the pressure data at each time instance to estimate STLE location. The \mname method produces accurate estimates even when (1) the STLE location is not bounded by two or more transducers or (2) when the STLE location is between two transducers that are situated several duct heights apart. Data from two direct-connect isolator models are used to evaluate the accuracy of the \mname method and demonstrate its robustness for different back-pressure scenarios and transducer configurations.

Robin L Hunt↗

Adaptive Pressure Profile Method to Locate the Isolator Shock Train Leading Edge Given Limited Pressure Information

To maximize the performance of high-speed air-breathing engines, such as dual-mode scramjets, the streamwise location of the shock train leading edge (STLE) is ideally placed as far upstream in the isolator as possible while avoiding engine unstart. Thus, it is of interest to quantify and control the STLE location as the vehicle travels along its flight trajectory. The STLE location is typically quantified using wall static pressure measurements but there are often restrictions on the number and placement of transducers, thus reducing the accuracy and overall capability of STLE detection methods. In this work, the Adaptive Pressure Profile (APP) method is introduced to address such sparsity concerns. This method is data driven and does not heavily rely on prior information about the flow regime or engine model. Instead, the \mname method uses real-time pressure measurements from a small number of transducers to adaptively learn the isolator pressure profile. This adaptively-learned profile is fit to the pressure data at each time instance to estimate STLE location. The \mname method produces accurate estimates even when (1) the STLE location is not bounded by two or more transducers or (2) when the STLE location is between two transducers that are situated several duct heights apart. Data from two direct-connect isolator models are used to evaluate the accuracy of the \mname method and demonstrate its robustness for different back-pressure scenarios and transducer configurations.

Robin Hunt↗

OFDM Radar Space-Time Adaptive Processing by Exploiting Spatio-Temporal Sparsity

We propose a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly-moving target using an orthogonal frequency division multiplexing (OFDM) radar. We observe that the target and interference spectra are inherently sparse in the spatio-temporal domain. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data and produces an equivalent performance as the other existing STAP techniques. In addition, the use of an OFDM signal increases the frequency diversity of our system, as different scattering centers of a target resonate at different frequencies, and thus improves the target detectability. First, we formulate a realistic sparse-measurement model for an OFDM radar considering both the clutter and jammer as the interfering sources. Then, we apply a residual sparse-recovery technique based on the LASSO estimator to estimate the target and interference covariance matrices, and subsequently compute the optimal STAP-filter weights. Our numerical results demonstrate a comparative performance analysis of the proposed sparse-STAP algorithm with four other existing STAP methods. Furthermore, we discover that the OFDM-STAP filter-weights are adaptable to the frequency-variabilities of the target and interference responses, in addition to the spatio-temporal variabilities. Hence, by better utilizing the frequency variabilities, we propose an adaptive OFDM-waveform design technique, and consequently gain a significant amount of STAP-performance improvement.

adaptive waveform design.↗

Fast Bayesian blind deconvolution with Huber Super Gaussian priors

We report expectation Maximization (EM) based inference has already proven to be a very powerful tool to solve blind image deconvolution (BID) problems. Unfortunately, three important problems still impede the application of EM in BID: the undesirable saddle points and local minima caused by highly nonconvex priors, the instability around zero of some of the most interesting sparsity promoting priors, and the intrinsic high computational cost of the corresponding BID algorithm. In this paper we first show how Super Gaussian priors can be made numerically tractable around zero by introducing the family of Huber Super Gaussian priors and then present a fast EM based blind deconvolution method formulated in the image space. In the proposed computational approach, image and kernel estimation are performed by using the Alternating Direction Method of Multipliers (ADMM), which allows to exploit the advantages of FFT computation. For highly nonconvex priors, we propose a Smooth ADMM (SADMM) approach to avoid poor BID estimates. In conclusion, extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art BID methods in terms of quality of the reconstructions and speed.

97 MATHEMATICS AND COMPUTING↗

Melting and phase relations of Fe-Ni-Si determined by a multi-technique approach

Many studies have suggested silicon as a candidate light element for the cores of Earth and Mercury. However, the effect of silicon on the melting temperatures of core materials and thermal profiles of cores is poorly understood, due to disagreements among melt detection techniques, uncertainties in sample pressure evolution during heating, and sparsity of studies investigating the combined effects of nickel and silicon on the phase diagram of iron. Here, in this study we develop a multi-technique approach for measuring the high-pressure melting and solid phase relations of iron alloys and apply it to Fe 0.8 Ni 0.1 Si 0.1 (Fe-11wt%Ni-5.3wt%Si), a composition compatible with recent estimates for the cores of Earth and Mercury. This approach combines results (20-83 GPa) from two atomic-level techniques: synchrotron Mossbauer spectroscopy (SMS) and synchrotron x-ray diffraction (XRD). Melting is independently detected by the loss of the Mossbauer signal, produced exclusively by solid-bound iron nuclei, and the onset of a liquid diffuse x-ray scattering signal. The use of a burst heating and background updating method for quantifying changes in the reference background during heating facilitates the determination of liquid diffuse signal onsets and leads to strong reproducibility and excellent agreement in melting temperatures determined separately by the two techniques. XRD measurements additionally constrain the hcp-fcc phase boundary and in-situ pressure evolution of the samples during heating. We apply our updated thermal pressure model to published SMS melting data on fcc-Fe and fcc-Fe 0.9 Ni 0.1 to precisely evaluate the effect of silicon on melting temperatures. We find that the addition of 10 mol% Si to Fe 0.9 Ni 0.1 reduces melting temperatures by ~250 K at low pressures (<60 GPa) and flattens the hcp-fcc phase boundary. Extrapolating our results, we constrain the location of the hcp-fcc-liquid quasi-triple point at 147±14 GPa and 3140±90 K, which implies a melting temperature reduction of 500 K compared with Fe 0.9 Ni 0.1 . The results demonstrate the advantages of combining complementary experimental techniques in investigations of melting under extreme conditions.

36 MATERIALS SCIENCE↗

A DATA EFFICIENT SPARSE MODELING FRAMEWORK FOR POWER ESTIMATION IN WATER TREATMENT SENSING OPERATIONS

With increasing freshwater scarcity, advanced process design mechanisms such as Closed-Circuit Reverse Osmosis (CCRO) and Digital/Physical Twin systems are gaining traction in water treatment and reuse operations. While digital and physical twin models enable improved system insight and control, their development is often expensive and computationally intensive, requiring large volumes of synthetic or experimental data to characterize underlying process dynamics. This work introduces a sparse surrogate modeling framework to estimate power consumption from measured flow and pressure variables, along with their nonlinear polynomial and interaction expansions. To ensure model reliability and reduce overfitting, a two-stage pipeline is proposed. First, a dynamic data filtering algorithm is employed to remove uninformative observations and transient operational states. Second, a sparse penalized regression technique is applied to select a minimal set of parsimonious features. The proposed model achieves high sparsity, retaining only 7 out of 34 candidate features (≈79.41% sparsity) while delivering a root mean square error (RMSE) of 0.072 on the test dataset.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗

Gaussian Process Regression under Computational and Epistemic Misspecification

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Furthermore, our theory also accounts for epistemic misspecification in the choice of kernel parameters.

Gaussian process regression↗

Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry

In this article, we provide an overview of state-of-the-art techniques that are being developed for efficient calculation of second and higher nuclear derivatives of quantum mechanical (QM) energy. Calculations of nuclear Hessians and anharmonic terms incur high costs and memory and scale poorly with system size. Three emerging classes of methods—machine learning (ML), automatic differentiation (AD), and matrix completion (MC)—have demonstrated promise in overcoming these challenges. We illustrate studies that employ unsupervised ML methods to reduce the need for multiple Hessian calculations in dynamics simulations and those that utilize supervised ML to construct approximate potential energy surfaces and estimate Hessians and anharmonic terms at reduced cost. By extension, if electronic structure operations could be written in a manner similar to functions underlying ML methods, rapid differentiation or AD routines can be employed to inexpensively calculate higher arbitrary-order derivatives. While ML approaches are typically black-box, we describe methods such as compressed sensing (CS) and MC, which explicitly leverage problem-specific mathematical properties of higher derivatives such as sparsity and low-rank, to complete higher derivative information using only a small, incomplete sample. The three classes of methods facilitate reliable predictions of observables ranging from infrared spectra to thermal conductivity and constitute a promising way forward in accurately capturing otherwise intractable higher-order responses of QM energy to nuclear perturbations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning

Purpose: This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality.Methods: First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of the objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency.Results: The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery.Conclusions: The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.

61 RADIATION PROTECTION AND DOSIMETRY↗

PowerMappeR: Power-Optimized Mapping of SNNs onto ReRAM Crossbars coupled via Packet-Switched NoCs

Many recent efforts in developing hardware-accelerated spiking neural networks (SNNs) are characterized by deep co-design between algorithms, architectures, and devices. Architectural advances overcome device constraints by coupling together many small resistive-RAM (ReRAM) crossbars via a network-on-chip (NoC) for neuromorphic component operation. Concurrently, improved SNN training methods increase accuracy and structural sparsity in networks despite growing problem sizes. Finally, compilers leverage these attributes to minimize area and inter-crossbar communication while mapping large SNNs to sophisticated architectures. However, for compiler-driven co-design to realize increasingly complex and profitable optimizations, a compile-time view of power consumption is critical. We present PowerMappeR to express and optimize over mapping-, architecture-, and device-specific power consumption information. By modeling the dynamic power of well-established components, we develop an integer linear programming (ILP)-based, encoding-agnostic, parametric power estimation model. Using this model, we demonstrate practical improvements in area and inter-crossbar communication by 0%–9.5% and 1.4%–5.1%, respectively. We also limit hotspot formation during optimization, achieving comparable or better results in targeted metrics with up to 96.4%–97.1% restriction of hotspot magnitude. Finally, we introduce profile-guided formulations to reduce worst-case and expected-case hotspot magnitude by 40.7%–69.5% and 40.6%–56.3%, respectively. Optimizing worst-case hotspot magnitude incidentally improves expected-case magnitude by 10.85%–33.45%. Reciprocally, optimizing expected-case magnitude incidentally improves worst-case magnitude by 4.33%–39.87%. Validation against hardware simulators confirms that PowerMappeR can decrease dynamic power consumption by 12.6%–27.3%.

Pohl, Devin [ORNL] (ORCID:0009000040149027)↗

A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. In this work, we introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

97 MATHEMATICS AND COMPUTING↗

A heterogeneous stochastic FEM framework for elliptic PDEs

We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sparse expansions of multicomponent oxide configuration energy using coherency and redundancy

We report that compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Introduction: Neuromorphic Materials

The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.

Circuits↗

Enhanced detection of paramagnetic fluorine-19 magnetic resonance imaging agents using zero echo time sequence and compressed sensing

Fluorine-19 ( 19 F) magnetic resonance imaging (MRI) is an emerging technique offering specific detection of labeled cells in vivo. Lengthy acquisition times and modest signal-to-noise ratio (SNR) makes three-dimensional spin-density–weighted 19 F imaging challenging. Recent advances in tracer paramagnetic metallo-perfluorocarbon (MPFC) nanoemulsion probes have shown multifold SNR improvements due to an accelerated 19 F T 1 relaxation rate and a commensurate gain in imaging speed and averages. However, 19 F T 2 -reduction and increased linewidth limit the amount of metal additive in MPFC probes, thus constraining the ultimate SNR. To overcome these barriers, we describe a compressed sampling (CS) scheme, implemented using a “zero” echo time (ZTE) sequence, with data reconstructed via a sparsity-promoting algorithm. Our CS-ZTE scheme acquires k-space data using an undersampled spherical radial pattern and signal averaging. Image reconstruction employs off-the-shelf sparse solvers to solve a joint total variation and -norm regularized least square problem. To evaluate CS-ZTE, we performed simulations and acquired 19 F MRI data at 11.7 T in phantoms and mice receiving MPFC-labeled dendritic cells. For MPFC-labeled cells in vivo, we show SNR gains of ~6.3 × with 8-fold undersampling. We show that this enhancement is due to three mechanisms including undersampling and commensurate increase in signal averaging in a fixed scan time, denoising attributes from the CS algorithm, and paramagnetic reduction of T 1 . Importantly, 19 F image intensity analyses yield accurate estimates of absolute quantification of 19 F spins. Overall, the CS-ZTE method using MPFC probes achieves ultrafast imaging, a substantial boost in detection sensitivity, accurate 19 F spin quantification, and minimal image artifacts.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Role of Updraft Velocity in Temporal Variability of Global Cloud Hydrometeor Number

Understanding how dynamical and aerosol inputs affect the temporal variability of hydrometeor formation in climate models will help to explain sources of model diversity in cloud forcing, to provide robust comparisons with data, and, ultimately, to reduce the uncertainty in estimates of the aerosol indirect effect. This variability attribution can be done at various spatial and temporal resolutions with metrics derived from online adjoint sensitivities of droplet and crystal number to relevant inputs. Such metrics are defined and calculated from simulations using the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) and the National Center for Atmospheric Research Community Atmosphere Model Version 5.1 (CAM5.1). Input updraft velocity fluctuations can explain as much as 48% of temporal variability in output ice crystal number and 61% in droplet number in GEOS-5 and up to 89% of temporal variability in output ice crystal number in CAM5.1. In both models, this vertical velocity attribution depends strongly on altitude. Despite its importance for hydrometeor formation, simulated vertical velocity distributions are rarely evaluated against observations due to the sparsity of relevant data. Coordinated effort by the atmospheric community to develop more consistent, observationally based updraft treatments will help to close this knowledge gap.

cloud condensation nuclei↗