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At least 343 records · Page 19

An automated cluster surface scanning method for exploring reaction paths on metal-cluster surfaces

Metal-cluster surfaces present a wide variety of unique coordination environments. This complexity makes it difficult to manually probe the surface reactivity of such clusters. Here, we present a simple and automated method to systematically discover reaction pathways on cluster surfaces, based on the automated cluster surface scanning (ACSS) technique for mapping out potential energy surfaces. We showcase our method on 55-atom icosahedral Cu and Ag clusters, where we determine the activation energies of four elementary steps common in heterogeneous catalysis – hydrogen recombination (H* + H* → H 2 * + *), oxygen recombination (O* + O* → O 2 * + *), water formation (OH* + H* → H 2 O* + *), and CO oxidation (CO* + O* → CO 2 * + *) – with density functional theory calculations (DFT-PBE + D3). We show that the ACSS method requires significantly less human effort than the established manually performed climbing-image nudged elastic band (MP + CI-NEB) technique and locates transition states with comparable accuracy (root-mean-squared error of 0.10 eV) and similar computational cost. Rigorous sampling of the potential energy surface with the ACSS method allows one to locate all lowest-energy reaction pathways obtained via the MP+CI-NEB approach, as well as alternative pathways that one may have missed with the MP+CI-NEB approach due to the many possible pathways available on these clusters. The accuracy and efficiency afforded by the ACSS method could enable high-throughput exploration of the diverse reactivity of metal clusters.

36 MATERIALS SCIENCE↗

Use of Satellite Data Assimilation to Infer Land Surface Thermal Inertia

There are two important but observationally uncertain parameters in the grid averaged surface energy budgets of mesoscale models - surface moisture availability and thermal heat capacity. A technique has been successfully developed for assimilating Geostationary Operational Environmental Satellite (GOES) skin temperature tendencies during the mid-morning time frame to improve specification of surface moisture. In a new application of the technique, the use of satellite skin temperature tendencies in early evening is explored to improve specification of the surface thermal heat capacity. Together, these two satellite assimilation constraints have been shown to significantly improve the characterization of the surface energy budget of a mesoscale model on fine spatial scales. The GOES assimilation without the adjusted heat capacity was run operationally during the International H2O Project on a 12-km grid. This paper presents the results obtained when using both the moisture availability and heat capacity retrievals in concert. Preliminary results indicate that retrieved moisture availability alone improved the verification statistics of 2-meter temperature and dew point forecasts. Results from the 1.5 month long study period using the bulk heat capacity will be presented at the meeting.

Lapenta, William↗

Novel Epoxy Particulate Composites for Mitigation of Insect Residue Adhesion on Future Aircraft Surfaces

Drag is reduced significantly for airflow over surfaces when laminar flow can be maintained over greater chord lengths, the distance from the leading edge of an airfoil.1 However, surface imperfections, such as chipped paint, scratches, and events that change topography on a microscopic scale can introduce airflow instabilities resulting in premature transition to turbulent flow.1 Although many of these surface imperfections can be avoided with proper maintenance, advanced materials, and advanced manufacturing practices, topographical surface anomalies arising during flight from insect impacts cannot be controlled and can influence laminar flow stability. Practical solutions to this operational challenge need to be developed for future aircraft to have full advantage of laminar flow designs that improve fuel efficiency.2 Researchers have investigated various methods to mitigate insect residue adhesion for decades.3 Although several techniques have demonstrated efficacy including mechanical scrapers, active liquid discharge systems, and sacrificial paper coatings, they have not been commercially implemented due to increased manufacturing and operational complexity, environmental impact, and weight penalties. Coatings offer a simple route for passive insect residue adhesion prevention without many of the challenges associated with maintenance of laminar flow.4 In our previous work, we determined that most commercially available materials were not effective at insect residue adhesion.5 We also identified improvements when both surface energy could be controlled by surface modifying agents and the topography could be altered through the use of micron-sized and nanometer-sized filler materials.6 In this work, these general principles were applied to an epoxy system to evaluate the behavior of the surface modifying agent, a fluorinated alkyl ether oligomer, on surface energy and insect residue adhesion properties.

Wohl, Christopher J.↗

Catalytic resonance theory: Circumfluence of programmable catalytic loops

Chemical reactions on heterogeneous catalyst surfaces exhibit complex networks of elementary reactions with multiple pathways to fluid phase products, sometimes leading to surface reaction loops consisting of a closed cycle reaction pathway. While conventional catalysts at steady state exhibit zero net flux in either direction around a catalytic loop, the loop turnover frequency of three-species surface loops was evaluated in this work via microkinetic modeling to assess the reaction loop behavior resulting from a catalytic surface oscillating between two or more surface energy states. For dynamic heterogeneous catalysts undergoing applied oscillations of surface energy (i.e., programs), surface reaction loops of three species were shown to exhibit non-zero net flow of molecules around the loop, with the extent of loop turnover frequency varying with the applied frequency and amplitude of a sinusoidal or square wave oscillation. Alternatively, some dynamic surface reactions exhibited oscillations only between two surface species or resulted in surfaces covered by a single species at all times. Here, more complex behavior was observed for dynamic surface programs of three distinct electronic states, with the temporal order of applied states controlling the direction of flow of molecules within a three-molecule surface loop. Catalytic loops have the potential to limit overall catalytic reaction rates and use energy in programmable catalysts, while some applications could purposely impose non-zero loop turnover frequency for improved surface reaction control.

Catalysis↗

The quantum dynamics of electronically nonadiabatic chemical reactions

Considerable progress was achieved on the quantum mechanical treatment of electronically nonadiabatic collisions involving energy transfer and chemical reaction in the collision of an electronically excited atom with a molecule. In the first step, a new diabatic representation for the coupled potential energy surfaces was created. A two-state diabatic representation was developed which was designed to realistically reproduce the two lowest adiabatic states of the valence bond model and also to have the following three desirable features: (1) it is more economical to evaluate; (2) it is more portable; and (3) all spline fits are replaced by analytic functions. The new representation consists of a set of two coupled diabatic potential energy surfaces plus a coupling surface. It is suitable for dynamics calculations on both the electronic quenching and reaction processes in collisions of Na(3p2p) with H2. The new two-state representation was obtained by a three-step process from a modified eight-state diatomics-in-molecules (DIM) representation of Blais. The second step required the development of new dynamical methods. A formalism was developed for treating reactions with very general basis functions including electronically excited states. Our formalism is based on the generalized Newton, scattered wave, and outgoing wave variational principles that were used previously for reactive collisions on a single potential energy surface, and it incorporates three new features: (1) the basis functions include electronic degrees of freedom, as required to treat reactions involving electronic excitation and two or more coupled potential energy surfaces; (2) the primitive electronic basis is assumed to be diabatic, and it is not assumed that it diagonalizes the electronic Hamiltonian even asymptotically; and (3) contracted basis functions for vibrational-rotational-orbital degrees of freedom are included in a very general way, similar to previous prescriptions for locally adiabatic functions in various quantum scattering algorithms.

Truhlar, Donald G.↗

The Influence of surface binding energy on sputtering in models of the sodium exosphere of Mercury

We have simulated the sodium (Na) exosphere of Mercury to show how the exosphere is affected by the assumed surface binding energy (SBE) of Na in the sputtered component. We constrained ion precipitation onto the surface using distributions for the cusp regions that are consistent with measurements by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging Fast Imaging Plasma Spectrometer instrument. We have simulated sputtering with SBEs of 0.27, 2.6, 4.4, and 7.9 eV, with the lowest value commonly used in exosphere models and the highest from recent molecular dynamics calculations for the Na-bearing feldspar end-member, albite. A gradual change in the exosphere is seen as the yield decreases and the ejecta energy increases with increasing SBE. We describe the corresponding exosphere source functions for ion sputtering (IS), as well as for the previously studied processes of micrometeoroid impact vaporization and photon-stimulated desorption (PSD), along with their release energy distributions and spatial distributions. We have summed the contributions of the various source processes to explain how and when the different sources can be distinguished by observations. The modeled exosphere scale heights range from 72 km for PSD to over 1000 km for IS using a SBE of 7.9 eV. We find that the processes responsible for generating Mercury's Na exosphere are separable by measuring line-of-sight column densities tangent to the planet at various altitudes and positions around the planet. Our initial results are consistent with the Na being sputtered from a high-SBE material such as feldspar, which has been predicted to be abundant on the Mercury's surface.

Rosemary M. Killen↗

Semiconductor surface sublimation energies and atom-atom interactions

The energy required to remove an atom from semiconductor surfaces is calculated using a Green's-function approach. Contrary to intuition, it is found that, in some cases, less energy is needed to remove an atom from the nearly full surface than from a nearly empty surface. The results are explained in terms of the relative energies of anion and cation dangling bonds, and the charge transfers between them. The deducted effective pair-interaction energies and their effects on surface morphology and growth perfection are discussed.

Krishnamurthy, Srinivasan↗

Regional Energy Budget Over Ocean Derived From Satellite Observations

The uncertainty in regional surface energy flux derived by summing all energy flux components is known to be large. In addition, quantifying the regional energy flux uncertainty considering all flux component uncertainties is very difficult. However, this approach is needed to understand regional energy flux components and how these components change with time. The CERES surface radiation budget data product, Edition 4.1 EBAF combined with reanalysis products was used to assess regional surface energy budget over ocean in earlier studies. The CERES team revised the data product and released Edition 4.2 EBAF product in February 2023. Prominent differences from the earlier edition are: 1) no geostationary satellite derived cloud properties are used for surface irradiance computations and 2) MERRA-2 provides temperature and humidity profiles. Combined with surface turbulent fluxes from various products, this study uses the revised EBAF surface irradiances and addresses regional energy budget over ocean. In addition, the uncertainty in regional surface radiation and energy budgets is discussed.

Seiji Kato↗

Protein Adhesion on Semi-Fluorinated Polystyrene Surfaces in Static and Dynamic Measurements

Reducing protein adhesion is a critical strategy in fouling-resistant material innovation, with broad applications spanning biomedical and healthcare devices, biosensors, industrial and environmental systems, and other important technological domains. Here, in this study, we elucidated protein adhesion behavior on polystyrene-based thin films by neutron reflectometry (NR) and quartz crystal microbalance with dissipation (QCM-D), using both lysozyme and bovine serum albumin (BSA) as model proteins. To this end, semifluorinated polystyrene thin films with gradient wettability and surface energy were fabricated through dry processing using plasma oxidation and gas-phase deposition. Although it is believed that a fully fluorinated alkyl chain offers extremely low surface energy, thus rejecting foulants, and has been used in many fouling-resistant surface designs, enhanced protein–surface interactions were observed consistently in NR and QCM-D results, due to the combined effects of surface morphology and chemistry. On the contrary, depositing shorter fluorinated silane onto a hydrophilic PS surface contributed to a more homogeneous nanoscale fluorine coating, resulting in less initial protein adsorption and improved surface recovery. Comparative analysis of proteins with different sizes on the nanopatterned semifluorinated surface revealed the influence of molecular characteristics on surface interactions. Lysozyme, being smaller and more compact, showed faster adsorption kinetics and higher surface coverage but largely reversible binding, whereas BSA, with its larger and more flexible structure, formed broader and more stable interfacial layers. This study fills the gap in understanding protein adhesion within the range of hydrophobicity (water contact angle ∼90°), as current strategies often associate with extreme hydrophilic and superhydrophobic surfaces due to hydration or low-surface-energy rejection mechanisms, respectively. It also provides in-depth insights into current combinatorial fouling-resistant surface design.

Yuan, Yue [Oak Ridge National Laboratory (ORNL), O↗

Development, Integration and Utilization of Surface Nuclear Energy Sources for Exploration Missions

Throughout the past five decades numerous studies have identified nuclear energy as an enhancing or enabling technology for human surface exploration missions. Nuclear energy sources were used to provide electricity on Apollo missions 12, 14, 15, 16, and 17, and on the Mars Viking landers. Nuclear energy sources were used to provide heat on the Pathfinder; Spirit, and Discovery rovers. Scenarios have been proposed that utilize -1 kWe radioisotope systems for early missions, followed by fission systems in the 10 - 30 kWe range when energy requirements increase. A fission energy source unit size of approximately 150 kWt has been proposed based on previous lunar and Mars base architecture studies. Such a unit could support both early and advanced bases through a building block approach.

Houts, Michael G.↗

Characteristics and radiolysis behavior of polyvinylchloride under accelerated proton and γ-irradiation

Here the effect of high energy protons and γ-irradiation on the structural properties, surface-energies, and toxicological properties of polyvinyl chloride (PVC) were studied due to the role PVC products play in many technologies including the nuclear industry. Accelerated 1–4 MeV protons impacting on PVC in vacuum lead to the formation of polyenyl radicals as shown by EPR and to an increase in free surface energy due to functionalization of the surface of the irradiated polymer. γ-irradiation leads to the formation of unsaturated bonds, carbonyl and hydroxyl groups as shown by IR and to the release of HCl. Correlated molecular orbital theory calculations of reaction thermodynamics were used to aid in the development of a mechanism in the absence of oxygen. The formation and accumulation of chromophores and auxochromic groups during γ-radiolysis of PVC leads to a gradual change of the initial white color of the polymer to yellow and then to brown and black with high sensitivity. A mixture of powdered PVC and silicate glue was used to determine the profile of a 60 Co γ-radiation beam on targets with a complex relief. γ-irradiated polymer does not have a local irritating effect due to a single application to the skin of mice in an adhesive mixture at a concentration of up to 5000 mg/kg. γ-radiolysis of PVC powder in air with a dose of up to 1400 kGy does not affect its acute toxicity when administered intragastrically to BDF1 mice. PVC and its γ-irradiated analogs are non-toxic at doses ≤5000 mg/kg.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Solar Wind Ion Sputtering of Sodium from Silicates Using Molecular Dynamics Calculations of Surface Binding Energies

For nearly 40 yr, studies of exosphere formation on airless bodies have been hindered by uncertainties in our understanding of the underlying ion collisional sputtering by the solar wind (SW). These ion impacts on airless bodies play an important role in altering their surface properties and surrounding environment. Much of the collisional sputtering data needed for exosphere studies come from binary collision approximation (BCA) sputtering models. These depend on the surface binding energy (SBE) for the atoms sputtered from the impacted material. However, the SBE is not reliably known for many materials important for planetary science, such as plagioclase feldspars and sodium pyroxenes. BCA models typically approximate the SBE using the cohesive energy for a monoelemental solid. We use molecular dynamics (MD) to provide the first accurate SBE data we are aware of for Na sputtered from the above silicate minerals, which are expected to be important for exospheric formation at Mercury and the Moon. The MD SBE values are ∼8 times larger than the Na monoelemental cohesive energy. This has a significant effect on the predicted SW ion sputtering yield and energy distribution of Na and the formation of the corresponding Na exosphere. We also find that the SBE is correlated with the coordination number of the Na atoms within the substrate and with the cohesive energy of the Na-bearing silicate. Our MD SBE results will enable more accurate BCA predictions for the SW ion sputtering contribution to the Na exosphere of Mercury and the Moon.

Lunar surface↗

Impact of Seasonal Snow-Cover Change on the Observed and Simulated State of the Atmospheric Boundary Layer in a High-Altitude Mountain Valley

The structure and evolution of the atmospheric boundary layer (ABL) under clear-sky fair weather conditions over mountainous terrain is dominated by the diurnal cycle of the surface energy balance and thus strongly depends on surface snow cover. We use data from three passive ground-based infrared spectrometers deployed in the East River Valley in Colorado's Rocky Mountains to investigate the response of the thermal ABL structure to changes in surface energy balance during the seasonal transition from low to high snow cover. Temperature profiles were retrieved from the infrared radiances using the optimal estimation physical retrieval Tropospheric Remotely Observed Profiling via Optimal Estimation. A nocturnal surface inversion formed in the valley during clear-sky days, which was subsequently mixed out during daytime with the development of a convective boundary layer when snow cover was low. Over high snow cover, a very shallow convective boundary layer formed, above which the inversion persisted through the daytime hours. We compare these observations to NOAA's operational High-Resolution-Rapid-Refresh model and find large warm biases on clear-sky days resulting from the model's inability to form strong nocturnal inversions and to maintain the stable stratification in the valley during daytime when there was snow on the ground. We suggest several factors contributing to the large model errors. These are (a) the inability of the model to represent well-developed thermally driven flows likely due to the too coarse horizontal grid spacing (3 km), (b) too much convective mixing during daytime, and (c) too strong vertical coupling between the valley atmosphere and the free troposphere.

54 ENVIRONMENTAL SCIENCES↗

The Heat of Formation of HNO

The HNO molecule is of interest in both combustion and atmospheric chemistry. For example, Guadagnini et al. have recently presented ab initio potential energy surfaces for the three lowest lying electronic states of HNO and then used these in examining several chemical reactions that take place in the combustion of nitrogen containing fuels and in the oxidation of atmospheric nitrogen. We have previously studied the ground state potential energy surface (i.e., stationary points along the HNO rev. reaction HON path), vibrational spectrum (using an accurate quartic force field), zero-point energy, and bonding of HNO using coupled-cluster ab initio methods. HNO is also very interesting because of the unique nature of its bonding characteristics. That is, the potential energy surface is very flat along the H-N bonding coordinate thereby giving unusual harmonic and fundamental vibrational frequencies, and the H-N bond energy is rather weak in comparison to other H-N bond energies. In fact, using experimental heats of formation for HO, H, and NO, the H- bond energy is computed to be only 49.9 kcal/ mol (298 K). However, ab initio calculations of isodesmic reaction energies involving HNO, FNO, ClNO, and several other molecules have shown that there is an inconsistency in the experimental heats of formation of the XNO (X=H, F, and Cl) species. Hence the motivation for this study was to determine a very accurate(DELTA)H(sup o)(sub f) value for HNO using state of-the-art ab initio methods. Based on many recent studies it is evident that the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), in conjunction with large one-particle basis sets should be reliable to better than +0.8 kcal/mol for this quantity. The computational methodology is described in the next section followed by our results and discussion. Conclusions are presented in the final section.

Lee, Timothy J.↗

The Heat of Formation of HNO

The HNO molecule is of interest in both combustion and atmospheric chemistry. For example, Guadagnini et al. have recently presented ab initio potential energy surfaces for the three lowest lying electronic states of HNO and then used these in examining several chemical reactions that take place in the combustion of nitrogen containing fuels and in the oxidation of atmospheric nitrogen. We have previously studied the ground state potential energy surface (i.e., stationary points along the HNO reversible reaction HON path), vibrational spectrum (using an accurate quartic force field), zero-point energy, and bonding of HNO using coupled-cluster ab initio methods. HNO is also very interesting because of the unique nature of its bonding characteristics. That is, the potential energy surface is very flat along the H-N bonding coordinate thereby giving unusual harmonic and fundamental vibrational frequencies, and the H-N bond energy is rather weak in comparison to other H-N bond energies. In fact, using experimental heats of formation for HNO, H, and NO, the H- bond energy is computed to be only 49.9 kcal/ mol (298 K). However, ab initio calculations of isodesmic reaction energies involving HNO, FNO, ClNO, and several other molecules have shown that there is an inconsistency in the experimental heats of formation of the XNO (X double bond H, F, and Cl) species. Hence the motivation for this study was to determine a very accurate (Delta)H(sub f, sup o) value for HNO using state-of-the-art ab initio methods. Based on many recent studies it is evident that the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), in conjunction with large one-particle basis sets should be reliable to better than +/- 0.8 kcal/mol for this quantity. The computational methodology is described in the next section followed by our results and discussion. Conclusions are presented in the final section.

Lee, Timothy J.↗

Land Surface Data Assimilation and the Gulf Coast Sea-Breeze

A technique has been developed for assimilating GOES-derived skin temperature tendencies and insolation into the surface energy budget equation of a mesoscale model so that the simulated rate of temperature change closely agrees with the satellite observations. A critical assumption of the technique is that the availability of moisture (either from the soil or vegetation) is the least known term in the model's surface energy budget. Therefore, the simulated latent heat flux, which is a function of surface moisture availability, is adjusted based upon differences between the modeled and satellite observed skin temperature tendencies. An advantage of this technique is that satellite temperature tendencies are assimilated in an energetically consistent manner that avoids energy imbalances and surface stability problems that arise from direct assimilation of surface shelter temperatures. The fact that the rate of change of the satellite skin temperature is used rather than the absolute temperature means that sensor calibration is not as critical. The focus of this paper is to examine how the satellite assimilation technique impacts simulations of near-surface meteorology on the 4- to 48-hour time scale. The technique is implemented within the PSU/NCAR MM5 V34 and applied on a 36-km CONUS domain and a 12-km nest centered over Oklahoma. Two Friday periods during 2000 were selected for study, one during the warm season (May-June) and the other in the cold season (Nov-Dec). Bulk verification statistics (BIAS and RMSE) of surface air temperature and dewpoint show that the assimilation technique can improve numerical simulations on both regional and continental scales. Comparison of the simulated surface energy and water fluxes with observations from Energy Balance Bowen Ratio measurements taken at CART/ARM sites in the Southern Great Plains showed the assimilation technique produces a realistic argument of the Bowen ratio in both seasons. Additional runs with the Oregon State University land surface scheme as implemented within MM5 will be made and comparisons with assimilation results will be presented at the meeting.

Lapenta, William M.↗

Assimilation of GOES Land Surface Data into a Mesoscale Models

A technique has been developed for assimilating Geostationary Operational Environmental Satellite (GOES)-derived skin temperature tendencies and insolation into the surface energy budget equation of a mesoscale model so that the simulated rate of temperature change closely agrees with the satellite observations. A critical assumption of the technique is that the availability of moisture (either from the soil or vegetation) is the least known term in the model's surface energy budget. Therefore, the simulated latent heat flux, which is a function of surface moisture availability, is adjusted based upon differences between the modeled and satellite-observed skin temperature tendencies. An advantage of this technique is that satellite temperature tendencies are assimilated in an energetically consistent manner that avoids energy imbalances and surface stability problems that arise from direct assimilation of surface shelter temperatures. The fact that the rate of change of the satellite skin temperature is used rather than the absolute temperature means that sensor calibration is not as critical. The assimilation technique has been applied to the Oklahoma-Kansas region during the spring-summer 2000 time period when dynamic changes in vegetation cover occur. In April, central Oklahoma is characterized by large NDVI associated with winter wheat while surrounding areas are primarily rangeland with lower NDVI. In July the vegetation pattern reverses as the central wheat area changes to low NDVI due to harvesting and the surrounding rangeland is greener than it was in April. The goal of this study is to determine if assimilating satellite land surface data can improve simulation of the complex spatial distribution of surface energy and water fluxes across this region. The PSU/NCAR NM5 V3 system is used in this study. The grid configuration consists of a 36-km CONUS domain and a 12-km nest over the area of interest. Bulk verification statistics (BIAS and RMSE) of surface air temperature and dewpoint indicates that assimilation of the satellite data results reduces both the bias and RMSE for both state variables. In addition, comparison of model data with ARM/CART EBBR flux observations reveals that the assimilation technique adjusts the bowen ratio in a realistic fashion.

Lapenta, William M.↗

High-Resolution Mesoscale Simulations of the 6-7 May 2000 Missouri Flash Flood: Impact of Model Initialization and Land Surface Treatment

High-resolution mesoscale model simulations of the 6-7 May 2000 Missouri flash flood event were performed to test the impact of model initialization and land surface treatment on timing, intensity, and location of extreme precipitation. In this flash flood event, a mesoscale convective system (MCS) produced over 340 mm of rain in roughly 9 hours in some locations. Two different types of model initialization were employed: 1) NCEP global reanalysis with 2.5-degree grid spacing and 12-hour temporal resolution, and 2) Eta reanalysis with 40- km grid spacing and $hour temporal resolution. In addition, two different land surface treatments were considered. A simple land scheme. (SLAB) keeps soil moisture fixed at initial values throughout the simulation, while a more sophisticated land model (PLACE) allows for r interactive feedback. Simulations with high-resolution Eta model initialization show considerable improvement in the intensity of precipitation due to the presence in the initialization of a residual mesoscale convective vortex (hlCV) from a previous MCS. Simulations with the PLACE land model show improved location of heavy precipitation. Since soil moisture can vary over time in the PLACE model, surface energy fluxes exhibit strong spatial gradients. These surface energy flux gradients help produce a strong low-level jet (LLJ) in the correct location. The LLJ then interacts with the cold outflow boundary of the MCS to produce new convective cells. The simulation with both high-resolution model initialization and time-varying soil moisture test reproduces the intensity and location of observed rainfall.

Baker, R. David↗