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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Anthropogenic Aerosols Contribute to the Recent Decline in Precipitation Over the U.S. Southwest

Abstract The winter‐spring precipitation over the Southwestern United States (SWUS) decreased since 1980. It is frequently attributed to Pacific internal decadal variability, but recent studies found anthropogenic aerosols (AA) can also induce a transition to a negative Pacific Decadal Variability (PDV) phase. We revisit the attribution of SWUS drying by quantifying the contributions of anthropogenically forced decadal Pacific Sea Surface Temperatures (SSTs). Applying a low‐frequency component analysis to observations, Community Earth System Model version 2 (CESM2) all‐forcings and single‐forcing large ensembles, we find up to 42% of the observed precipitation trend to be related to the AA‐induced negative PDV‐like pattern, which is driven by the emission shift from the Western to the Eastern Hemisphere. In CESM2, other radiative forcings counteract the influence of AA, but it remains unclear whether the model correctly simulates this balance. This implies that the near‐future trajectories of these forcings, in particular Asian aerosols, are important for projections of SWUS precipitation.

Geology↗
DOE OSTI2026

Regional Earthquake Ground Motion Simulations for Southern California With EQSIM: Insights From the 2008 Chino Hills, 2024 Highland Park, and 2021 Carson Earthquakes

This study presents physics-based, 3D simulations using the EQSIM framework for several earthquakes in the Los Angeles region. The primary objective was to assess the ability of deterministic physics-based ground motion simulations to reproduce the observed motions from historical events. The selected events included the mathematical equation M w 5.4 2008 Chino Hills, the mathematical equation M w 4.4 2024 Highland Park, and the mathematical equation M w 4.3 2021 Carson events. The simulated motions were evaluated by comparing the recorded and simulated seismograms, as well as the Fourier amplitude spectra, across multiple seismic stations. The SCEC 3D velocity model, CVM-S4.26.M01, was used to represent the regional geology, and ground motion simulations were carried out with a resolution of up to 5 Hz. The results indicate that the simulated motions captured the recorded motions up to approximately 4 Hz. While careful iterations regarding source parameters and corner frequencies were required, and, for the case of the Highland Park event, some of the near-source stations had relatively low accuracy, the present study established a positive step toward the utilization of physics-based simulations in practical applications. The computational efficiencies exhibited by EQSIM, especially on GPU clusters, further supported this assertion, as wall-clock times of simulations involving more than 10 billion grid points were as low as mathematical equation minutes. This permits ensemble simulations for a considered scenario event so that modeling uncertainties (e.g., source and geology) can be bracketed.

EQSIM↗
DOE OSTI2024

FORESTR: Finding, Organizing, Representing, Explaining, Summarizing, and Thinning Random forests

Random forests have become popular models used for data driven predictions. As a result, random forests are currently used or being considered for high-consequence mission applications in national security, such as the prediction of yield from optical signals and malware detection. While random forests may provide accurate predictions, the complexity of the algorithm causes a lack of interpretability. Random forests are an ensemble of regression or decision trees. Individual regression and decision trees are interpretable, but ensembles are inherently difficult to interpret due to the compilation of many models. We aim to increase the interpretability of random forests by finding patterns in the ensemble of trees that can be used to “thin” (or remove) trees. As a starting point, in this report, we develop a new distance metric for quantifying the similarity between trees based on their topologies (i.e., shapes). We base the metric on a novel distance metric for graphs that is a proper mathematical distance, is invariant to transformations, has registration between graphs, and computes topological evolutions between graphs. We use the tree distance metric to compute tree statistics such as a “mean tree” and to identify clusters of trees. We apply the developed methodology to a toy dataset and a mission relevant product inspection dataset to demonstrate how the metric can provide insight into random forests. Furthermore, we discuss the limitations of the approach and ideas for future research into how the metric could be used as a thinning tool to develop less complex models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Ensemble transfer learning for the prediction of anti-cancer drug response

Abstract Transfer learning, which transfers patterns learned on a source dataset to a related target dataset for constructing prediction models, has been shown effective in many applications. In this paper, we investigate whether transfer learning can be used to improve the performance of anti-cancer drug response prediction models. Previous transfer learning studies for drug response prediction focused on building models to predict the response of tumor cells to a specific drug treatment. We target the more challenging task of building general prediction models that can make predictions for both new tumor cells and new drugs. Uniquely, we investigate the power of transfer learning for three drug response prediction applications including drug repurposing, precision oncology, and new drug development, through different data partition schemes in cross-validation. We extend the classic transfer learning framework through ensemble and demonstrate its general utility with three representative prediction algorithms including a gradient boosting model and two deep neural networks. The ensemble transfer learning framework is tested on benchmark in vitro drug screening datasets. The results demonstrate that our framework broadly improves the prediction performance in all three drug response prediction applications with all three prediction algorithms.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Evolution of the Antarctic Ice Sheet from 2000–2300 and beyond: model sensitivity and uncertainty analysis using MPAS-Albany Land Ice

We present a description of the Antarctic Ice Sheet model configuration submitted to the ISMIP6-Antarctica-2300 experiment using the MPAS-Albany Land Ice model, along with three new sets of simulations: (1) a set of extended simulations to 2500 for three forced experiments and to 2775 for the control experiment; (2) a sensitivity analysis of our model configuration to parameters controlling basal sliding and sub-shelf melt, and to model structural choices including the choice of the energy and stress balances; and (3) a 72-member ensemble run on graphics processing units (GPUs) and analysis of variance to determine the primary sources of uncertainty in our ice-sheet model projections. Our extended simulations predict rapid retreat beginning after 2300 for SSP1-2.6 forcing and after 2500 for present-day (control) forcing, primarily in the Amundsen Sea Embayment. We find that varying the sub-shelf melt parameter between the 5th to 95th percentile values for a mean-Antarctic calibration target results in an up to ∼ ± 40 % change in sea-level contribution relative to our baseline simulations that used the median value. Using a linear basal sliding law reduces sea-level contribution by 51 %–73 % relative to our baseline nonlinear sliding law with an exponent of 1/5. When using basal sliding law exponents of 1/3 and 1/10, the overall difference from our baseline simulations at 2300 is on the order of 10 %. The Amundsen Sea Embayment region displays a strongly non-linear dependence of mass loss on the sliding law exponent, with no discernible relationship between the sliding law exponent and the mass loss by 2300, while the sectors feeding the Ross and Filchner-Ronne ice shelves exhibit more mass loss with a more-plastic sliding law. Our model fidelity sensitivity experiments reveal a 9 %–31 % increase in sea-level contribution when using a depth-integrated stress balance approximation relative to our three-dimensional solver, while using a fixed-in-time temperature field increases sea-level contribution by 14 %–88 % relative to two thermomechanically coupled configurations. Our 72-member ensemble and analysis of variance show that the uncertainty in long-term projections is dominated by the choice of Earth system model forcing and the presence or absence of hydrofracture forcing, rather than uncertainty in sliding and sub-shelf melt parameters.

58 GEOSCIENCES↗
DOE OSTI2021

Dynamic Interconversion of Metal Active Site Ensembles in Zeolite Catalysis

Catalysis science is founded on understanding the structure, number, and reactivity of active sites. Kinetic models that consider active sites to be static and noninteracting entities are routinely successful in describing the behavior of heterogeneous catalysts. Yet, active site ensembles often restructure in response to their external environment and even during steady-state catalytic turnover, sometimes requiring non-mean-field kinetic treatments to describe distance-dependent interactions among sites. Such behavior is being recognized more frequently in modern catalysis research, with the advent of experimental methods to quantify turnover rates with increasing precision, an expanding arsenal of operando characterization tools, and computational descriptions of atomic structure and motion at chemical potentials and timescales increasingly relevant to reaction conditions. This review focuses on dynamic changes to metal active site ensembles on zeolite supports, which are silica-based crystalline materials substituted with Al that generate binding sites for isolated and low-nuclearity metal site ensembles. Metal sites can become solvated and mobilized during reaction, facilitating interactions among sites that change their nuclearity and function. Such intersite communication can be regulated by the zeolite support, resulting in non-single-site and potentially non-mean-field kinetic behavior arising from mechanisms of catalytic action that combine elements of those canonically associated with homogeneous and heterogeneous catalysis. Here, we discuss recent literature examples that document dynamic active site behavior in metal-zeolites and outline methodologies to identify and interpret such behavior. We conclude with our outlook on future research directions to develop this evolving branch of catalysis science and harness it for practical applications.

operando characterization↗
DOE OSTI2024

Real-time capable modeling of ICRF heating on NSTX and WEST via machine learning approaches

Abstract A real-time capable core Ion Cyclotron Range of Frequencies (ICRF) heating model on NSTX and WEST is developed. The model is based on two nonlinear regression algorithms, the random forest ensemble of decision trees and the multilayer perceptron neural network. The algorithms are trained on TORIC ICRF spectrum solver simulations of the expected flat-top operation scenarios in NSTX and WEST assuming Maxwellian plasmas. The surrogate models are shown to successfully capture the multi-species core ICRF power absorption predicted by the original model for the high harmonic fast wave and the ion cyclotron minority heating schemes while reducing the computational time by six orders of magnitude. Although these models can be expanded, the achieved regression scoring, computational efficiency and increased model robustness suggest these strategies can be implemented into integrated modeling frameworks for real-time control applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Identifying Robust Decarbonization Pathways for the Western U.S. Electric Power System Under Deep Climate Uncertainty

Climate change threatens the resource adequacy of future power systems. Existing research and practice lack frameworks for identifying decarbonization pathways that are robust to climate-related uncertainty. We create such an analytical framework, then use it to assess the robustness of alternative pathways to achieving 60% emissions reductions from 2022 levels by 2040 for the Western U.S. power system. Our framework integrates power system planning and resource adequacy models with 100 climate realizations from a large climate ensemble. Climate realizations drive electricity demand; thermal plant availability; and wind, solar, and hydropower generation. Among five initial decarbonization pathways, all exhibit modest to significant resource adequacy failures under climate realizations in 2040, but certain pathways experience significantly less resource adequacy failures at little additional cost relative to other pathways. By identifying and planning for an extreme climate realization that drives the largest resource adequacy failures across our pathways, we produce a new decarbonization pathway that has no resource adequacy failures under any climate realizations. This new pathway is roughly 5% more expensive than other pathways due to greater capacity investment, and shifts investment from wind to solar and natural gas generators. Our analysis suggests modest increases in investment costs can add significant robustness against climate change in decarbonizing power systems. Our framework can help power system planners adapt to climate change by stress testing future plans to potential climate realizations, and offers a unique bridge between energy system and climate modeling.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Detecting tropospheric composition and climate responses to US air pollution controls in the context of internally-arising variability

Since the 1970s, air pollutant emissions controls in the United States (US) have lowered concentrations of ozone (O 3 ) and aerosols, which have opposing radiative effects on surface temperature. Using a pair of initial-condition ensembles generated by a fully-coupled chemistry-climate model, we simulate the “world avoided” by US air pollution controls. In this counterfactual world, we find tropospheric column O 3 increases, robust to natural internal variability, extending across the Northern Hemisphere. Robust aerosol increases, dominated by sulfate, remain localized near the US. Wintertime Northwest Atlantic cloud droplet number concentration is particularly sensitive to US aerosol. While an ensemble mean US surface cooling signal (−0.4 °C) implies that aerosol-driven cooling prevails over any O 3 -induced warming, we find that large regional internal variability will confound its detection in any single transient realization. Larger signal-to-noise ratios for composition versus climate variables underscore the greater detectability of emissions-driven changes in tropospheric composition compared to their associated climate impacts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Enhancing Extreme Precipitation Predictions With Dynamical Downscaling: A Convection‐Permitting Modeling Study in Texas and Oklahoma

Precipitation in the Southern Plains of the United States is relatively well depicted by the Community Earth System Model (CESM). However, despite its ability to capture seasonal mean precipitation anomalies, CESM consistently underestimates extreme pluvial and drought events, rendering it an insufficient tool for extending simulation lead times for exceptional events, such as the abnormally dry May 2011, which helped drive Texas into its worst period of drought in more than a century, and the abnormally wet May 2015, which led to widespread flooding in that state. Ensemble‐based regional climate experiments are completed for the two extreme years using Weather Research and Forecasting model (WRF) and downscaled from CESM. WRF simulations are at convection‐permitting grid resolution for improved physical representation of simulated precipitation over the Southern Great Plains. By integrating convection‐permitting models (CPMs) into each individual member of a CESM ocean data assimilation ensemble, this study demonstrates that high‐resolution dynamical downscaling can improve model skillfulness at capturing these two events and is thus a potentially useful tool for forecasting extremely high and extremely low precipitation events at subseasonal or even seasonal lead times.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Historical evaluation and future projections of compound heatwave and drought extremes over the conterminous United States in CMIP6 *

Abstract Independently, both droughts and heatwaves can induce severe impacts on human and natural systems. However, when these two climate extremes occur concurrently in a given region, their compound impacts are often more pronounced. With the improvement in both the spatiotemporal resolution and representation of complex climate processes in the global climate models (GCMs), they are increasingly used to study future changes in these extremes and associated regional impacts. However, GCM selection for such impact assessments is generally based on historical performance and/or future mean changes, without considering individual or compound extremes. In contrast, this study evaluates historical performance and projected changes in heatwaves, droughts, and compound heatwave-droughts using an ensemble of GCMs from the latest Phase 6 of Coupled Models Intercomparison Project at a regional scale across the conterminous United States. Additionally, we explore the inter-model differences in the projected changes that are associated with various characteristics of extremes and the choice of drought indices. Our analysis reveals considerable variation among the GCMs, as well as substantial differences in the projected changes based on the choice of drought indices and region of interest. For example, the projected increases in both the frequency and intensity of drought and associated compound extreme days, based on the standardized precipitation evapotranspiration index far exceed those derived from the standard precipitation index. Further, the largest changes in the frequency of compound extremes are projected over the Southwest, South Central, and parts of the Southeast while the smallest changes are projected over the Northeast. Overall, this study provides important insights for the interpretation and selection of GCMs for future assessment studies that are crucial for the development of regional adaptation strategies in the face of climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Overview of the Nephele Perturbed Parameter Ensemble for Aerosol‐Cloud Interactions in E3SMv3

Aerosol-cloud interactions (aci) are the leading source of uncertainty in inferring climate sensitivity from the historical record. Earth system models (ESMs) struggle to represent aci because the processes responsible for these phenomena occur at much finer time and space scales than can be resolved by any ESM. Observational constraints provide key benchmarks to test ESMs, but cannot be used alone to fully understand aci processes except in very specific cases where causality is controlled; some degree of modeling is required to infer aci and estimate radiative forcing. Here, we generate and characterize a perturbed parameter ensemble (PPE) in version 3 of the Energy Exascale ESM (E3SMv3). We perturb 25 parameters that govern aci processes over 250 members and integrate the model over present-day and preindustrial aerosol emissions. We find that the process representation in E3SMv3 is flexible and can generate global-mean effective radiative forcings due to aci (ERFaci) ranging from −3.0 to +0.9 W m −2 . The positive ERFaci values simulated by a portion of the PPE are implausible and result from parameter combinations that produce unrealistic top-of-atmosphere energy fluxes. While global-mean cloud droplet number concentration always increases in response to anthropogenic aerosol, cloud liquid water path can both increase and decrease, suggesting that precipitation suppression is not the only aerosol-cloud adjustment represented by E3SMv3. Analysis of which processes control liquid cloud adjustment in the PPE points toward stratiform precipitation processes and aerosol activation, which is consistent with many previous ESMs, as well as the new two-moment convective cloud microphysics in E3SMv3.

Nugent, Jacqueline M. [Univ. of Wyoming, Laramie, ↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Decomposing Cloud Radiative Feedbacks by Cloud-Top Phase

Changes in cloud scattering properties and emissivity that arise from atmospheric warming cause substantial radiative feedbacks in model projections of anthropogenic climate change, and the relative importance of the underlying mechanisms is poorly understood. One leading hypothesis is that ice-to-liquid conversions cause clouds to optically thicken, producing a major negative feedback. We test this hypothesis by developing a method to decompose cloud radiative feedbacks by cloud-top phase. The method is applied to an ensemble of six state-of-the-art global climate models run with prescribed sea surface temperature. In these simulations, the global mean of the net cloud scattering and emissivity feedback from cloud-phase conversions ranges from −0.17 to −0.01 W m −2 K −1 , while the overall net cloud feedback ranges from 0.02 to 0.91 W m −2 K −1 . The multimodel mean of the cloud scattering and emissivity feedback from cloud-phase conversions is approximately 19% of the magnitude of the multimodel mean of the overall cloud feedback (−0.10 vs 0.52 W m −2 K −1 ). These results indicate that cloud-phase conversions cause a robust negative feedback by changing cloud scattering and emissivity, but this mechanism makes a modest contribution to the overall cloud feedback at the global scale.

Climate change↗
DOE OSTI2025

Aerosol-Cloud Interactions and the Intersection of Climate Forcing and Feedback

The goal of this project has been to understand at the process level how the interaction of aerosols and cloud microphysics may alter the cloud response to climate change from the scale of turbulence to the global scale. Atmospheric aerosols (suspended particulates) have a unique role to play in the climate system. Anthropogenic aerosols may be an air pollution hazard and degrade human health. Their presence also results in the direct scattering or absorption of sunlight, with small net impacts on climate. But aerosols are also a key part of cloud formation, as the locations on which cloud droplets and ice crystals form. Understanding these Aerosol Cloud Interactions (ACI) is a critical uncertainty for climate models, including the Energy Exascale Earth System Model (E3SM), and affects how well models like E3SM can simulate the past and future. This work aims to understand cloud microphysics as well as the interaction of aerosol forcing and cloud feedback through improving our understanding of aerosol-cloud interactions (ACI) by looking at their uncertainty in critical environments at the process level. It will also contribute to the development of E3SM. Specific goals include: first, high level analysis of Perturbed Parameter Ensemble (PPE) simulations already available from the Community Earth System Model (CESM) and E3SM. Second, detailed analysis of recent changes to temperature and the role of aerosols.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Metal hydride composition-derived parameters as machine learning features for material design and H 2 storage

Though hydrogen is a promising energy carrier for a green future, many challenges persist. One is the difficulty in engineering storage solutions, with metal hydrides being a leading contender among solid-state strategies. To facilitate efficient searching of candidate materials, ridge regression, simple decision trees, random forest ensembles, and gradient boosting ensembles were employed to predict the energy of formation, with the random forest ensemble resulting in the lowest test set error. First, two public databases, Materials Project and HydPark, were searched for metal hydrides. Feature engineering was performed before the models were developed, resulting in electronegativity, density, atomic density, d-character, f-character, band gap, hydrogen weight fraction, magnetization, temperature, and pressure being retained. The models were then benchmarked by the lowest test error before a random forest ensemble was used to populate entries missing energy of formation. Furthermore, all were then scored by hydrogen storage capacity and energy of formation suitability. Readily available features including several derived from only the chemical formula which were found to be highly predictive. and so are promising for high-throughput screening of arbitrary novel hydride formulations and blends for thermodynamic feasibility.

25 ENERGY STORAGE↗
DOE OSTI2020

Radiative heating rate profiles over the southeast Atlantic Ocean during the 2016 and 2017 biomass burning seasons

Marine boundary layer clouds, including the transition from stratocumulus to cumulus, are poorly represented in numerical weather prediction and general circulation models. Further uncertainties in the cloud structure arise in the presence of biomass burning carbonaceous aerosol, as is the case over the southeast Atlantic Ocean, where biomass burning aerosol is transported from the African continent. As the aerosol plume progresses across the southeast Atlantic Ocean, radiative heating within the aerosol layer has the potential to alter the thermodynamic environment and therefore the cloud structure; however, limited work has been done to quantify this along the trajectory of the aerosol plume in the region. The deployment of the first Atmospheric Radiation Measurement (ARM) Mobile Facility (AMF1) in support of the Layered Atlantic Smoke Interactions with Clouds field campaign provided a unique opportunity to collect observations of cloud and aerosol properties during two consecutive biomass burning seasons during July through October of 2016 and 2017 over Ascension Island (7.96° S, 14.35° W). Using observed profiles of temperature, humidity, and clouds from the field campaign alongside aerosol optical properties from Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), as input for the Rapid Radiation Transfer Model (RRTM), profiles of the radiative heating rate due to aerosols and clouds were computed. Radiative heating is also assessed across the southeast Atlantic Ocean using an ensemble of back trajectories from the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model. Idealized experiments using the RRTM with and without aerosols and a range of values for the single-scattering albedo (SSA) demonstrate that shortwave (SW) heating within the aerosol layer above Ascension Island can locally range between 2 and 8 K d -1 depending on the aerosol optical properties, though impacts of the aerosol can be felt elsewhere in the atmospheric column. When considered under clear conditions, the aerosol has a cooling effect at the TOA, and based on the observed cloud properties at Ascension Island, the cloud albedo is not large enough to overcome this. Shortwave radiative heating due to biomass burning aerosol is not balanced by additional longwave (LW) cooling, and the net radiative impact results in a stabilization of the lower troposphere. However, these results are extremely sensitive to the single-scattering albedo assumptions in models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Factors Affecting Entrainment Rate in Deep Convective Clouds and Parameterizations

The parameterization of cloud entrainment rates has been problematic for many years, hindering the accurate representation of convective processes in large-scale models. Here, we extend our previous work on individual shallow convection to ensemble deep convection. Entrainment rates are estimated based on three-dimensional convective clouds from August 19-20 of 1999, during the Kwajalein Experiment, simulated using a high-resolution cloud-resolving model. They are found to be negatively correlated with both vertical velocity and buoyancy, and positively correlated with the vertical divergence of the vertical velocity and with the reciprocal of cloud radii. The physical mechanisms underlying these relationships are interpreted. It is found that the parameterizations with multiple properties perform better than those with a single property. Entrainment rates and relative humidity of entrained air are positively correlated at temperature higher than 0°C, but negatively correlated at temperature lower than 0°C. Relative humidity is also included in the parameterization of entrainment rates, which differs from our previous work on shallow cumulus clouds and other studies. Finally, two forms of parameterization for entrainment rate are recommended. The first treats the entrainment rate as a function of the vertical velocity and buoyancy for temperature higher than 0°C, but as a function of relative humidity and buoyancy for temperature lower than 0°C. The second involves an equation that relates entrainment rates to vertical velocity and buoyancy regardless of temperature.

54 ENVIRONMENTAL SCIENCES↗