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At least 505 records · Page 28

Stochastic modal velocity field in rough-wall turbulence

Stochastically generated instantaneous velocity profiles are used to reproduce the outer region of rough-wall turbulent boundary layers in a range of Reynolds numbers extending from the wind tunnel to field conditions. Each profile consists in a sequence of steps, defined by the modal velocities and representing uniform momentum zones (UMZs), separated by velocity jumps representing the internal shear layers. Height-dependent UMZ is described by a minimal set of attributes: thickness, mid-height elevation, and streamwise (modal) and vertical velocities. These are informed by experimental observations and reproducing the statistical behaviour of rough-wall turbulence and attached eddy scaling, consistent with the corresponding experimental datasets. Sets of independently generated profiles are reorganized in the streamwise direction to form a spatially consistent modal velocity field, starting from any randomly selected profile. The operation allows one to stretch or compress the velocity field in space, increases the size of the domain and adjusts the size of the largest emerging structures to the Reynolds number of the simulated flow. By imposing the autocorrelation function of the modal velocity field to be anchored on the experimental measurements, we obtain a physically based spatial resolution, which is employed in the computation of the velocity spectrum, and second-order structure functions. The results reproduce the Kolmogorov inertial range extending from the UMZ and their attached-eddy vertical organization to the very-large-scale motions (VLSMs) introduced with the reordering process. The dynamic role of VLSM is confirmed in the –u'w' co-spectra and in their vertical derivative, representing a scale-dependent pressure gradient contribution.

42 ENGINEERING↗

Asymptotic coefficients of the attached-eddy model derived from an adiabatic atmosphere

The attached-eddy model (AEM) predicts that the mean streamwise velocity and streamwise velocity variance profiles follow a logarithmic shape, while the vertical velocity variance remains invariant with height in the overlap region of high Reynolds number wall-bounded turbulent flows. Moreover, the AEM coefficients are presumed to attain asymptotically constant values at very high Reynolds numbers. Here, the AEM predictions are examined using sonic anemometer measurements in the near-neutral atmospheric surface layer, with a focus on the logarithmic behaviour of the streamwise velocity variance. Utilizing an extensive 210-day dataset collected from a 62 m meteorological tower located in the Eastern Snake River Plain, Idaho, USA, the inertial sublayer is first identified by analysing the measured momentum flux and mean velocity profiles. The logarithmic behaviour of the streamwise velocity variance and the associated ‘−1’ scaling of the streamwise velocity energy spectra are then investigated. The findings indicate that the Townsend–Perry coefficient (A 1 ) is influenced by mild non-stationarity that manifests itself as a Reynolds number dependence. After excluding non-stationary runs, and requiring the bulk Reynolds number defined using the atmospheric boundary layer height to be larger than 4 × 10 7 , the inferred A 1 converges to values ranging between 1 and 1.25, consistent with laboratory experiments. Furthermore, nine benchmark cases selected through a restrictive quality control reveal a close relation between the ‘−1’ scaling in the streamwise velocity energy spectrum and the logarithmic behaviour of streamwise velocity variance. However, additional data are required to determine whether the plateau value of the pre-multiplied streamwise velocity energy spectrum is identical to A 1 .

atmospheric flows↗

Mechanically induced localisation of SECONDARY WALL INTERACTING bZIP is associated with thigmomorphogenic and secondary cell wall gene expression

Plant growth requires the integration of internal and external cues, perceived and transduced into a developmental programme of cell division, elongation and wall thickening. Mechanical forces contribute to this regulation, and thigmomorphogenesis typically includes reducing stem height, increasing stem diameter, and a canonical transcriptomic response. We present data on a bZIP transcription factor involved in this process in grasses. Brachypodium distachyon SECONDARY WALL INTERACTING bZIP (SWIZ) protein translocated into the nucleus following mechanostimulation. Classical touch-responsive genes were upregulated in B. distachyon roots following touch, including significant induction of the glycoside hydrolase 17 family, which may be unique to grass thigmomorphogenesis. SWIZ protein binding to an E-box variant in exons and introns was associated with immediate activation followed by repression of gene expression. SWIZ overexpression resulted in plants with reduced stem and root elongation. These data further define plant touch-responsive transcriptomics and physiology, offering insights into grass mechanotranduction dynamics.

Coomey, Joshua↗

Advanced Method Optimization with Categorical and Constrained Continuous Parameters

Traditional approaches to analytical method optimization (e.g., univariate and “guess-and-check”) can be time-consuming, costly, and often fail to identify true optima within the parameter space. Previous work defined and implemented a generalized technique for method optimization for continuous method parameters, but a knowledge gap remains for the incorporation of categorical variables into these advanced method optimization schemes. This work presents and validates a generalized optimization approach that incorporates both continuous and categorical variables while also utilizing a multivariate, multiobjective optimization scheme with Karush–Kuhn–Tucker conditions to bound the optimization space to solutions within the physical limitations of the parameter space. Method optimization from a case study using GC–MS for the analysis of 11 analytical standards with objectives to minimize peak width and maximize peak height resulted in a 3 orders of magnitude improvement in the average peak height and a 2 orders of magnitude improvement in the average peak width compared to the least optimal (but reasonable) instrumental parameters utilized in this study. This approach to optimization allows for a customizable method optimization in which users can include both continuous and categorical variables to achieve objectives specific to their analytical goals. This approach significantly reduces the labor and cost associated with traditional method development approaches and can be applied in a variety of scientific fields across a range of laboratory techniques (e.g., instrument method development, sample preparation, and extraction techniques).

Amorphous materials↗

Crystal Growth and Elemental Homogeneity of the Multicomponent Rare-Earth Garnet (Lu 1/6 Y 1/6 Ho 1/6 Dy 1/6 Tb 1/6 Gd 1/6 ) 3 Al 5 O 12

We report high-entropy aluminum garnets were grown as bulk single crystals using the micro-pulling-down method, taking the synthesis of complex ceramics a step further from the conventional preparation of polycrystalline materials. We studied the effects of growth parameters on the elemental distribution in high optical quality crystals of (Lu 1/6 Y 1/6 Ho 1/6 Dy 1/6 Tb 1/6 Gd 1/6 ) 3 Al 5 O 12 containing six cations (yttrium and rare-earths) taken in equimolar amounts. A single garnet structure was confirmed by powder X-ray diffraction. Electron microprobe measurements were obtained to correlate the radial distribution of rare-earth elements with pulling rates and molten zone height. The nature of the elemental distribution in the radial direction was associated with ionic radius: smaller rare-earths concentrated in the center of the crystal, while larger rare-earths segregated toward the outer edge of the cylindrical crystal. Faster pulling rates led to a flattening of the concentration profiles toward the nominal concentration, promoting a more homogeneous radial elemental distribution, while varying the molten zone height did not have a significant effect. The demonstrated success with crystal growth enables the practical availability of single crystals of multicomponent aluminum garnets for further discovery of new phenomena and applications.

36 MATERIALS SCIENCE↗

Discrepancies between Theory and Experiment in Determining the Ionization Energy of NF 3

High-accuracy ab initio thermochemical predictions for the ionization energy of NF 3 , the barrier height (to inversion) of NF 3 + , and the dissociative ionization threshold of NF 3 to NF 2 + + F are presented and incorporated into Active Thermochemical Tables. The adiabatic ionization energy of the first ionization band of NF 3 , calculated at 12.647 ± 0.010 eV, is at odds with previous experimental interpretations by nearly 0.36 eV due to unfavorable Franck-Condon factors associated with this transition. The barrier (to inversion) height is calculated to be about 0.6 eV lower in energy than the prior interpretation, which instigates a discussion of the supposed vibrational structure of the first ionization band of NF 3 . Updated assignments of the photoelectron spectrum are proposed, and the loss in vibrational spacing on the high-energy side of the experimental ionization band is discussed. Rudimentary anharmonic Franck-Condon simulations qualitatively reproduce the broad spectral features observed in experiment.

Active Thermochemical Tables↗

Pb Sorption at the Barite (001)–Water Interface

Sorption of ions at the mineral-water interface is an important factor that determines the fate of toxic metals in the environment. Here, we use barite as a model substrate to understand the interaction of toxic-metal lead (Pb) with ionic crystals. The coverage and location of Pb sorbed to the (001) surface was measured as a function of aqueous Pb concentration ([Pb] aq ) using in situ specular resonant anomalous X-ray reflectivity (RAXR) to determine the sorption capacity and process. In this work, the results show that Pb sorption occurs via incorporation (primarily within the top barite layer similar to 3 angstrom in depth) and adsorption (mostly as an inner-sphere complex at similar to 2 angstrom in height) simultaneously. Both the incorporated and adsorbed Pb coverages increase with increasing [Pb] aq up to [Pb] aq similar to 200 mu M, above which the adsorbed fraction increases more rapidly than the incorporated fraction. This enhanced adsorption has a height distribution that is further extended (>= 15 angstrom from the surface) than that observed in lower [Pb] aq . This change in distribution is interpreted as arising from additional sorption of outer-sphere species or Pb-bearing phases precipitated on the surface. Desorption experiments in Pb-free solutions show that the incorporated fraction is more resistant to removal than the adsorbed fraction, consistent with the speciation-dependent stabilities premised in the classical sorption models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unravelling Adsorbate-Metal-Oxide Interactions: Water Vapor Chemistry on the Growth and Sintering of Ni over Reducible CeO2(111) Thin Films

The role of water in the growth and sintering of Ni particles over well-ordered CeOx(111) (1.5 < x < 2) thin films was investigated through scanning tunneling microscopy (STM) and X-ray photoelectron spectroscopy (XPS) studies, considering ceria-supported Ni attracts great attention as a promising catalyst for reactions such as steam reforming of ethanol and water gas shift reaction, in which water vapor is used as a key reactant. In the study, both fully oxidized CeO2 and partially reduced CeO1.75 thin films were prepared to examine the effect of the oxygen vacancies/Ce3+ sites in ceria supports. Our STM results revealed that dosing water before or after Ni deposition over the CeOx(111) surfaces at room temperature influenced the sintering behavior of Ni nanoparticles with further heating. Exposure of water to Ni nanoparticles that were deposited over both CeO2 and CeO1.75 at 300 K causes the formation of flatter particles with significantly reduced height when heating to the same temperatures compared to Ni/ceria with no water adsorbates. The flatter Ni particles were also observed when water was first dosed over CeO2 at 300 K followed by Ni deposition at room temperature and further heating. Over a partially reduced CeO1.75 surface with predosed water at 300 K, there is an extensive decrease in the particle density upon subsequent Ni deposition at room temperature and a significant increase in the height for Ni nanoparticles with further heating to higher temperatures compared to Ni over a pristine CeO1.75 surface. This is due to the filling of oxygen vacancies caused by the dissociation of water. This creates fewer nucleation sites for Ni on ceria, weakening the metal-oxide interaction and causing significant metal sintering. Our experimental findings suggest distinct adsorbate-metal-oxide interactions are key to the tuning of sintering of Ni nanoparticles over the CeOx(111) surface caused by water exposure. Such interactions are essential for the further modification of Ni-based catalysts for improved reactivity and stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

All-Atom Molecular Dynamics Simulations of the Temperature Response of Densely Grafted Polyelectrolyte Brushes

Water acts a “good” solvent for most polyelectrolyte (PE) systems due to its high dielectric strength. Theoretical and experimental studies have highlighted some remarkably unconventional properties of strongly water-swollen PE brushes such as a reduction in brush height with increase in temperature. However, an understanding of the atomistic-scale response of the grafted PE chains as well as the local arrangement and organization of the brush-supported counterions and water molecules to changes in temperature is missing. Here, we conduct an all-atom molecular dynamics (MD) study to probe the influence of temperature on the “microstructure” of densely grafted, fully ionized polyacrylic acid (PAA) brushes. The atomistic insights obtained from our study shed light on prior experimental observations and elucidate the key role played by changes in hydrogen bonding network in dictating the hydrophilicity of the brushes. In addition to the temperature-mediated reduction in height of the PE brush layer, we study the influence of temperature on several properties of the brush-supported water molecules such as the number distribution and kinetics of water-water and water-PE hydrogen bonds (HBs), mass density, orientational tetrahedral order parameter, and the activation energy associated with the self-diffusion of water. The effect of temperature on the properties of the brush-trapped counterions is also quantified via changes in their solvation structure, counterion-water radial distribution function (RDF), and the translational mobility. Our findings unravel several hitherto unknown phenomena such as the enhanced propensity for attaining PE brush-induced “water-in-salt”-like scenarios at elevated temperatures, and an increase in the activation energy for the self-diffusion of water with increase in the degree of PE brush-induced nanoconfinement (from ‘bulk water’ to ‘sparsely grafted PE brushes’ to ‘densely grafted PE brushes’). Further, we anticipate that this work will be helpful in improving our predictive capabilities of the temperature response of water-swollen PE brushes, which would be instrumental for better design of several PE brush systems used in a multitude of applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Charge-Density-Specific Response of Grafted Polyelectrolytes to Electric Fields: Bending or Tilting?

The response of polyelectrolytes (PEs) to applied electric fields drive applications in energetics, diagnostics, materials development, and many more. Here we employ all-atom molecular dynamics (MD) simulations to probe the response of grafted PE brushes to axial electric fields. For PEs with large charge densities, the electric field triggers a left-right asymmetric distribution of counterions around the PE backbone: consequently, depending on the location (left or right), there is an unequal screening and an unequal force on the PE functional groups causing a bending-driven brush height reduction. However, for the weakly charged PEs, the electric field causes a uniform distribution of the counterions across the brush enforcing a uniform (without left-right asymmetry) partially unscreened PE brush: therefore, all the brush segments experience similar force causing a brush tilting-driven brush height reduction. As a result, such bending versus tilting responses is commensurate with the electric-field-driven increase (decrease) in the flexibility of strongly (weakly) charged PEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dissolvable Template Nanoimprint Lithography: A Facile and Versatile Nanoscale Replication Technique

Nanoimprinting lithography (NIL) is a next-generation nanofabrication method, capable of replicating nanostructures from original master surfaces. In this work, we develop highly scalable, simple, and nondestructive NIL using a dissolvable template. Termed dissolvable template nanoimprinting lithography (DT-NIL), our method utilizes an economic thermoplastic resin to fabricate nanoimprinting templates, which can be easily dissolved in simple organic solvents. Additionally, we used the DT-NIL method to replicate cicada wings which have surface nanofeatures of ~100 nm in height. The master, template, and replica surfaces showed a >~94% similarity based on the measured diameter and height of the nanofeatures. The versatility of DT-NIL was also demonstrated with the replication of re-entrant, multiscale, and hierarchical features on fly wings, as well as hard silicon wafer-based artificial nanostructures. The DT-NIL method can be performed under ambient conditions with inexpensive materials and equipment. Our work opens the door to opportunities for economical and high-throughput nanofabrication processes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Optimization of Delignified Wood Rods for Interfacial Solar Evaporation

Interfacial solar evaporation using three-dimensional evaporator materials has shown promise to achieve high evaporation rates exceeding the photothermal limit for water treatment and resource recovery processes. However, challenges remain in optimizing the material geometry to balance the vertical capillary uptake of water and the rate of evaporation to achieve both stable and high evaporation rates. Delignified wood can serve as a highly porous and hydrophilic substrate material to achieve high evaporation rates. In this work, we designed a suspended biochar-coated delignified wood rod evaporator and investigated the influence of its geometric parameters on its evaporation performance. The height of the evaporator exposed to air for evaporation was observed to be an important parameter in governing the evaporation rate, as shorter evaporators limited the available surface area for evaporation, but taller evaporators could not achieve sufficient rates of capillary uptake to maintain stable evaporation rates over 24 h under 1-sun illumination (1 kW m –2 ). In conclusion, the exposed height of the evaporator was optimized to achieve an average hourly evaporation rate of 3.05 ± 0.23 kg m –2 h –1 , which could be maintained in saline solutions containing up to 5 wt % NaCl.

Coating materials↗

Incorporating Diurnal and Meter-Scale Variations of Ambient CO 2 Concentrations in Development of Direct Air Capture Technologies

To be implemented on climate-relevant scales, direct air capture of CO 2 (DAC) will require large capital-intensive facilities and careful attention to cost minimization. In making decisions among potential sites for DAC facilities, all of the factors that will impact process cost and efficiency should be considered. In this paper we focus on a factor that has previously received little attention in the DAC community, namely variations in atmospheric conditions on hourly time scales and length scales of meters. We present data curated from extensive previous studies of biosphere-atmosphere fluxes with observations of CO 2 concentration, temperature, and relative humidity (RH) with hourly resolution from many sites in North America. These include locations where typical diurnal variations in CO 2 concentration during summer months exceeds 150 ppm. These variations are larger than the seasonal variations that exist between averaged CO 2 concentrations in winter and summer, and they are highly correlated with diurnal variations in temperature and RH. Diurnal variations are dependent on the height above ground at which CO 2 concentrations are measured, with smaller variations existing at heights of 10 m or more than at ground level. We illustrate the potential implications of these short-term variations for the operation and optimization of a DAC process with process-level calculations for a specific adsorption-based process using amine-rich adsorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploring topography-based methods for downscaling subgrid precipitation for use in Earth System Models

Topography exerts major control on land surface processes. To improve representation of topographic impacts on land surface processes, a new topography-based subgrid structure has been introduced to the Energy Exascale Earth System Model to represent the subgrid heterogeneity of surface elevation. To take advantage of the new subgrid structure for improving land surface modeling, this study explores four variations of topography-based methods for downscaling grid precipitation to the corresponding subgrids. In the first three methods, the deviation of the subgrid precipitation from the grid’s is equal to the grid precipitation multiplied by the ratio of the elevation difference between the subgrid and grid mean to a specified elevation equals to the grid elevation, the difference between the maximum and minimum subgrid elevation, and the maximum subgrid elevation, respectively. The second method limits the ratio to 0.5 to avoid extreme values on mountains and the third method accounts for the slope effect. The fourth method is similar to the third method except that the Froude Number is used to limit the numerator in a blocking regime of the ambient flow. The downscaled precipitation is evaluated using the PRISM precipitation data over the U.S. using statistical metrics. Results show that by accounting for topographic slope besides elevation, the third and fourth methods show clear advantages over the first and second methods. Furthermore, introducing the Froude Number in the fourth method improves downscaling skill and shows consistent advantages over the third method in areas with larger subgrid heterogeneity across different grids sizes.

Tesfa, Teklu K.↗

Quantifying long-term seasonal and regional impacts of North American fire activity on continental boundary layer aerosols and cloud condensation nuclei

An intimate knowledge of aerosol transport is essential in reducing the uncertainty of the impacts of aerosols on cloud development. Datasets from the U. S. Department of Energy (DOE) Atmospheric Radiation Measurement platform in the Southern Great Plains region (ARM-SGP) and the NASA Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2) showed seasonal increases in aerosol loading and total carbon concentration during the spring and summer months (2008-2016) which was attributed to fire activity and smoke transport within North America. The monthly mean MERRA-2 surface carbonaceous aerosol mass concentration and ARM-SGP total carbon products were strongly correlated (R=0.82, p<0.01) along with a moderate correlation with the ARM-SGP cloud condensation nuclei (N CCN ) product (0.5, p~0.1). The monthly mean ARM-SGP total carbon and N CCN products were strongly correlated (0.7, p~0.01). An additional product denoting fire number and coverage taken from the National Interagency Fire Center (NIFC) showed a moderate correlation with the MERRA-2 carbonaceous product (0.45, p<0.01) during the 1981-2016 warm season months (March-September). With respect to meteorological conditions, the correlation between the NIFC fire product and MERRA-2 850 hPa isobaric height anomalies was lower (0.26, p~0.13) due to the variability in the frequency, intensity, and number of fires in North America. An observed increase in the isobaric height anomaly during the past decade may lead to frequent synoptic ridging and drier conditions with more fires, thereby potentially impacting cloud/precipitation processes and decreasing air quality.

54 ENVIRONMENTAL SCIENCES↗

An Observational Comparison of Level of Neutral Buoyancy and Level of Maximum Detrainment in Tropical Deep Convective Clouds

Tropical deep convective clouds are important drivers of large-scale atmospheric circulation representing the main vertical transport pathway through the depth of the troposphere for heat, momentum, water, and chemical species. The strength and depth of this transport are impacted by the convective updraft size and intensity that are driven by buoyancy, dynamical forcing, and mixing of environmental air, i.e., entrainment. In this paper, we identify tropical deep convective systems with well-defined forward anvils using Atmospheric Radiation Measurement (ARM) ground-based profiling radars, at three ARM fixed-sites in the Tropical Western Pacific (TWP; i.e., Manus, Nauru, Darwin) and three ARM Mobile Facility deployments in Niamey, Niger; Gan Island, Maldives; and Manacapuru, Brazil. We use the difference between the level of neutral buoyancy (LNB) and the level of maximum detrainment (LMD) as a proxy for the effective bulk convective entrainment (εproxy). The LNB, the theoretical height that a parcel raised above the level of free convection would reach with no mixing, is calculated based on pre-convection radiosonde measurements using parcel theory. The LMD is the height of the maximum reflectivity observed in forward anvil clouds by profiling radars. Deep convective systems over the TWP show higher LNBs that extend to 16.3 km on average and larger εproxy (median LNB minus LMD up to 6.5 km) compared to their continental counterparts in the Amazon and West Africa. Oceanic conditions show larger convective available potential energy (CAPE) coupled with higher moisture at low levels which favors larger εproxy. In contrast, continental cases initiate and develop under high convective inhibition, steeper environmental lapse rate, and high wind shear conditions, which show smaller offset between LNB and LMD. Deep convective cases that promote significant cold pools at the surface experience less εproxy. Using a Random Forest regression algorithm, CAPE is associated with the highest feature importance score for predicting convective εproxy, followed by low-level relative humidity. For continental cases, the low-level wind shear also indicates higher importance.

54 ENVIRONMENTAL SCIENCES↗

The Global Teleconnection Signature of the Madden-Julian Oscillation and Its Modulation by the Quasi-Biennial Oscillation

Recent research has suggested that the tropical and extratropical character of the Madden-Julian oscillation (MJO) depends on the state of the stratospheric quasi-biennial oscillation (QBO). With this in mind, we use both reanalysis and a global climate model (CESM2-WACCM) to analyze the global character of upper tropospheric-lower stratospheric geopotential height anomalies connected with the MJO and quantify dependencies of these teleconnections on the state of the QBO. We find that the global teleconnection signature of the MJO depends upon the state of the QBO. Globally, within reanalysis the fraction of 20- to 90-day 250-hPa geopotential height variance linked to the MJO is largest during boreal winter and summer for easterly QBO phases and smallest during westerly QBO phases of boreal winter. The difference between QBO phases is mostly driven by changes in the tropical signature of the MJO, although during boreal winter the Northern Hemispheric teleconnections are particularly more prominent during easterly QBO phases. Otherwise, the QBO modulation of extratropical MJO teleconnections is mainly realized through changes in the locations of the teleconnections. A QBO-MJO relationship is also apparent within CESM2-WACCM but is weaker than that observed. This extratropical modulation implies that the regions that benefit from increased subseasonal predictability due to the MJO may also change as a function of the QBO. In a broader sense, these findings emphasize that knowledge of the tropical stratospheric state, particularly as it relates to the QBO, is important for understanding the connections between the MJO and the extratropics.

54 ENVIRONMENTAL SCIENCES↗

A New Approach for Simultaneous Estimation of Entrainment and Detrainment Rates in Non- Precipitating Shallow Cumulus

A new approach is developed for estimating entrainment and detrainment rates in cumulus clouds based on aircraft observations. Equations relating entrainment and detrainment rates to gross entrainment and detrainment are derived. This approach is applied to the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems field campaign, supported by the U.S. Department of Energy's Atmospheric Radiation Measurement program. The results show that both entrainment and detrainment rates decrease with increasing height. Sensitivity tests with different detrained air assumptions yield similar results. The entrainment and detrainment rates can reproduce the cloud thermodynamic variables. Partial correlation analysis indicates that entrainment rate is positively correlated with environmental relative humidity (RH), and detrainment rate is negatively correlated with environmental RH and positively correlated with entrainment rate. This new approach can be applied to other cloud observations to obtain a data set of entrainment and detrainment rates in cumulus clouds.

Zhu, Lei↗