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At least 19 records

Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Mesoscale Convective Systems Represented in High Resolution E3SMv2 and Impact of New Cloud and Convection Parameterizations

Mesoscale convective systems (MCSs) play an important role in modulating the global hydrological cycle, general circulation, and radiative energy budget. In this study, we evaluate MCS simulations in the second version of U.S. Department of Energy (DOE) Energy Exascale Earth System Model (E3SMv2). E3SMv2 atmosphere model (EAMv2) is run at the uniform 0.25? horizontal resolution. We track MCSs consistently in the model and observations using the PyFLEXTRKR algorithm, which defines MCS based on both cloud-top brightness temperature (Tb) and surface precipitation. Results from using Tb only to define MCS, commonly used in previous studies, are also discussed. Furthermore, sensitivity experiments are performed to examine the impact of new cloud and convection parameterizations developed for EAMv3 on simulated MCSs. Our results show that EAMv2 simulated MCS precipitation is largely underestimated in the tropics and contiguous United States. This is mainly attributed to the underestimated precipitation intensity in EAMv2. In contrast, the simulated MCS frequency becomes more comparable to observations if MCSs are defined only based on cloud-top Tb. The Tb-based MCS tracking method, however, includes many cloud systems with very weak precipitation which conflicts with the MCS definition. This result illustrates the importance of accounting for precipitation in evaluating simulated MCSs. We also find that the new physics parameterizations help increase the relative contribution of convective precipitation to total precipitation in the tropics, but the simulated MCS properties are generally not improved. This suggests that simulating MCSs will remain a challenge for the next version of E3SM.

Zhang, Meng↗

An Optimized Parameterization of Sub‐Grid Scale Advection for Convection Permitting Models

Convection‐permitting models (CPMs) explicitly resolve deep convection yet under‐resolve the organized lateral exchanges among drafts and their environment that control entrainment/detrainment, precipitation efficiency, and mesoscale structure. In this work, we introduce the Optimized Advection Scheme (OAS), which introduces a small rotation of the Cartesian frame of reference for the horizontal winds relative to other variables used in advection that induces cross‐gradient transport to mimic under‐resolved convective mixing. The rotation angle is selected to minimize the Kullback–Leibler divergence between the simulated and satellite observed precipitation intensity distributions, yielding a physically consistent perturbation that is computationally inexpensive and portable. Optimized Advection Scheme is implemented in WRF and evaluated over Amazon (April 2014). It shifts precipitation–precipitable‐water joint distributions toward lighter rain, reduces overly intense rates, and improves mesoscale convective system (MCS) lifetime and propagation. Mechanistically, the added cross‐gradient transport promotes convective detrainment and environmental mixing, which cools and moistens the mid‐troposphere, weakens downward momentum transport, alleviates excessive downwelling shortwave biases, and warms the surface temperature. The optimized rotation angle yields comparable improvements at 4‐km and 1‐km grid spacing, demonstrating resolution‐independent benefits across the CPM gray zone. By targeting the dynamical root of under‐mixed convective circulations, rather than tuning model microphysics or closures, OAS delivers robust, scale‐aware improvements in precipitation statistics, cloud vertical structure, and characteristics of MCS (MCSs), offering a practical pathway to more reliable CPM simulations for weather and climate applications.

CPM↗

Kinetic Modeling of Secondary Organic Aerosol in a Weather-Chemistry Model: Parameterizations, Processes, and Predictions for GOAmazon

Secondary organic aerosol (SOA) forms and evolves in the atmosphere through many pathways and processes, over diverse spatial and time scales. Hence, there is a need to represent these widely-varying kinetic processes in large-scale atmospheric models to allow for accurate predictions of the abundance, properties, and impacts of SOA. In this work, we integrated a kinetic, process-level model (simpleSOM-MOSAIC) into a weather-chemistry model (WRF-Chem) to simulate the oxidation chemistry and microphysics of atmospheric SOA. simpleSOM-MOSAIC simulates multigenerational gas-phase chemistry, autoxidation reactions, heterogeneous oxidation, oligomerization, and phase-state-influenced gas/particle partitioning of SOA. As a case study, the integrated WRF-Chem-simpleSOM-MOSAIC (WC-SSM) model was used to simulate the photochemical evolution downwind of a large city (Manaus, Brazil) in the Amazon and, in turn, study the anthropogenic and biogenic interactions in an otherwise pristine environment. Consistent with previous work, we found that OA was enhanced by up to a factor of four in the urban plume due to elevated hydroxyl radical (OH) concentrations, relative to the background, and that this OA was dominated by SOA from biogenic precursors (80%). Further, in addition to accurately simulating the OA enhancement in the urban plume, the model reproduced the magnitude of the OA oxygen-to-carbon (O:C) ratio and broadly tracked the evolution of the aerosol size distribution. Our work highlights the importance of including an integrated, kinetic representation of SOA processes in an atmospheric model

54 ENVIRONMENTAL SCIENCES↗

Data for KETCHUP: Parameterizing of Large-Scale Kinetic Models Using Multiple Datasets with Different Reference States

Repository for Kinetic Estimation Tool Capturing Heterogeneous Datasets Using Pyomo (KETCHUP), a flexible parameter estimation tool that leverages a primal-dual interior-point algorithm to solve a nonlinear programming (NLP) problem that identifies a set of parameters capable of recapitulating the steady-state fluxes and concentrations in wild-type and perturbed metabolic networks. KETCHUP can use K-FIT [2] input files. Example K-FIT input files are located in the K-FIT repository at https://github.com/maranasgroup/K-FIT.

Metabolomics↗

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties With Deep Learning Multi‐Member and Stochastic Parameterizations

Abstract Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi‐member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi‐member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout‐based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best‐performing multi‐member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth‐like simulations but enables model stability over 5 months with our multi‐member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi‐member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi‐member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Behrens, Gunnar [Deutsches Zentrum für Luft‐ und R↗

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. Here, we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

97 MATHEMATICS AND COMPUTING↗

Memory-based parameterization with differentiable solver: Application to Lorenz ’96

Physical parameterizations (or closures) are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These parameterizations are typically grounded on physically based, yet empirical, representations of the underlying small-scale processes. Machine learning-based parameterizations have recently been proposed as an alternative solution and have shown great promise to reduce uncertainties associated with the parameterization of small-scale processes. Yet, those approaches still show some important mismatches that are often attributed to the stochasticity of the considered process. This stochasticity can be due to coarse temporal resolution, unresolved variables, or simply to the inherent chaotic nature of the process. To address these issues, we propose a new type of parameterization (closure), which is built using memory-based neural networks, to account for the non-instantaneous response of the closure and to enhance its stability and prediction accuracy. We apply the proposed memory-based parameterization, with differentiable solver, to the Lorenz ’96 model in the presence of a coarse temporal resolution and show its capacity to predict skillful forecasts over a long time horizon of the resolved variables compared to instantaneous parameterizations. This approach paves the way for the use of memory-based parameterizations for closure problems.

Mathematics↗

Cluster-dynamics-based parameterization for sulfuric acid–dimethylamine nucleation: comparison and selection through box and three-dimensional modeling

Clustering of gaseous sulfuric acid (SA) enhanced by dimethylamine (DMA) is a major mechanism for new particle formation (NPF) in polluted atmospheres. However, uncertainty remains regarding the SA–DMA nucleation parameterization that reasonably represents cluster dynamics and is applicable across various atmospheric conditions. This uncertainty hinders accurate three-dimensional (3-D) modeling of NPF and the subsequent assessment of its environmental and climatic impacts. Here we extensively compare different cluster-dynamics-based parameterizations for SA–DMA nucleation and identify the most reliable one through a combination of box model simulations, 3-D modeling, and in situ observations. Results show that the parameterization derived from Atmospheric Cluster Dynamic Code (ACDC) simulations, incorporating the latest theoretical insights (DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-311++G(3df,3pd) level of theory) and adequate representation of cluster dynamics, exhibits dependable performance in 3-D NPF simulation for both winter and summer conditions in Beijing and shows promise for application in diverse atmospheric conditions. Another ACDC-derived parameterization, replacing the level of theory with RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6–311++G(3df,3pd), also performs well in NPF modeling at relatively low temperatures around 280 K but exhibits limitations at higher temperatures due to inappropriate representation of SA–DMA cluster thermodynamics. Additionally, a previously reported parameterization incorporating simplifications is applicable for simulating NPF in polluted atmospheres but tends to overestimate particle formation rates under conditions of elevated temperature (>∼300 K) and low-condensation sink (<∼3×10 -3 s −1 ). Our findings highlight the applicability of the new ACDC-derived parameterization, which couples the latest SA–DMA nucleation theory and holistic cluster dynamics, in 3-D NPF modeling. The ACDC-derived parameterization framework provides a valuable reference for developing parameterizations for other nucleation systems.

Shen, Jiewen↗

Implementation of a Three-Dimensional Planetary Boundary Layer Parameterization in a Coupled Modeling System and Evaluation of "Gray Zone" Simulations of a Wind-Wave Event Off the US California Coast Using Observations

A three-dimensional (3D) planetary boundary layer (PBL) parameterization was added to the Coupled Ocean Atmosphere Wave Sediment Transport (COAWST) model and the first coupled atmosphere/wave "gray zone" simulations were carried out using the 3D PBL parameterization. A case study of a significant wind-wave event from 4-8 November 2020 off the US west coast was examined, with a focus on the impacts of the event within an approximate 280x280 km central California coastal region covering the Bureau of Ocean Energy Management Morro Bay wind energy lease area. Simulations with both one-dimensional (1D; Yonsei University) and 3D PBL parameterizations were examined in this nest with ..delta..x=400 m. Two-way coupling was active, with near-surface winds feeding back to the wave model and bulk wave statistics feeding back to the atmospheric model. Both simulations compared favorably with buoy observations in capturing the timing and magnitude of wind speed, temperature, dewpoint, and significant wave height, as the front associated with the maritime weather system moved southward across coastal California. However, wind speed errors over land were larger. Time series of the vertical profile of winds below z=250 m from the simulations compared favorably with observations from the US Dept. of Energy Morro Bay Doppler lidar buoy. Differences between the coupled 1D and 3D PBL simulations were minor. The most notable difference was that the simulation using the 3D PBL parameterization had approximately 10 % weaker winds at the peak of the event causing 10 % lower significant wave heights. This difference was shown to be mostly due to differences in the vertical mixing treatment between the parameterizations, in particular the nonlocal downward mixing of higher momentum air in the 1D Yonsei University parameterization in convective conditions. Overall, this work demonstrates that the 3D PBL parameterization can be used in a coupled atmosphere/wave modeling framework with similar behaviors as traditional PBL parameterizations that do not provide horizontal turbulent variances and fluxes.

16 TIDAL AND WAVE POWER↗

Parameterization and Explicit Modeling of Cloud Microphysics: Approaches, Challenges, and Future Directions

Cloud microphysical processes occur at the smallest end of scales among cloud-related processes and thus must be parameterized not only in large-scale global circulation models (GCMs) but also in various higher-resolution limited-area models such as cloud-resolving models (CRMs) and large-eddy simulation (LES) models. Instead of giving a comprehensive review of existing microphysical parameterizations that have been developed over the years, this study concentrates purposely on several topics that we believe are understudied but hold great potential for further advancing bulk microphysics parameterizations: multi-moment bulk microphysics parameterizations and the role of the spectral shape of hydrometeor size distributions; discrete vs “continuous” representation of hydrometeor types; turbulence-microphysics interactions including turbulent entrainment-mixing processes and stochastic condensation; theoretical foundations for the mathematical expressions used to describe hydrometeor size distributions and hydrometeor morphology; and approaches for developing bulk microphysics parameterizations. Also presented are the spectral bin scheme and particle-based scheme (especially, super-droplet method) for representing explicit microphysics. Their advantages and disadvantages are elucidated for constructing cloud models with detailed microphysics that are essential to developing processes understanding and bulk microphysics parameterizations. Particle-resolved direct numerical simulation (DNS) models are described as an emerging technique to investigate turbulence-microphysics interactions at the most fundamental level by tracking individual particles and resolving the smallest turbulent eddies in turbulent clouds. Outstanding challenges and future research directions are explored as well.

54 ENVIRONMENTAL SCIENCES↗

Data Imbalance, Uncertainty Quantification, and Transfer Learning in Data‐Driven Parameterizations: Lessons From the Emulation of Gravity Wave Momentum Transport in WACCM

Abstract Neural networks (NNs) are increasingly used for data‐driven subgrid‐scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non‐linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large‐amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN‐based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics‐based gravity wave (GW) parameterizations as a test case. WACCM has complex, state‐of‐the‐art parameterizations for orography‐, convection‐, and front‐driven GWs. Convection‐ and orography‐driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto‐encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO 2 ). However, their performance is significantly improved by applying transfer learning, for example, re‐training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data‐driven parameterizations for various processes, including (but not limited to) GWs.

54 ENVIRONMENTAL SCIENCES↗

A riming‐dependent parameterization of scattering by snowflakes using the self‐similar Rayleigh–Gans approximation

Abstract Riming is a key process of precipitation formation in ice‐containing clouds, but quantifying riming from observations is challenging, limiting our ability to evaluate the riming process in numerical weather models. One challenge for radar observations is that riming changes both the physical properties (mass, area cross‐section) and scattering properties of ice particles. These changes need to be implemented consistently as a function of riming in radar forward operators, which are required for retrievals and model evaluation in observation space. In this study, mass–size, cross‐section area–size, and backscattering cross‐section relations are developed as a function of the normalized rime mass for aggregates composed of various monomer types (columns, dendrites, needles, plates, and rosettes). The proposed framework allows us to simulate scattering properties of aggregated ice particles consistently as a function of riming in retrievals and radar forward operators. The parameterizations are developed from a large data set of simulated rimed aggregates of different sizes and monomer crystal types. The backscattering cross‐section parameterization (the “riming‐dependent parameterization”) is evaluated for radar frequencies of 35.6 and 94.0 GHz and is based on the Self‐Similar Rayleigh–Gans approximation (SSRGA), which is increasingly used to calculate microwave scattering of ice crystals and snowflakes. Compared with parameterizations from the literature that do not consider riming, the riming‐dependent parameterization leads to significantly smaller biases in terms of backscattering cross‐section. When using the particle masses and scattering properties of the individual particles simulated by the aggregation and riming model as a reference, the bias of our parameterization is below 1 dB when integrating over an exponential particle size distribution with sizes from 0.1–10 mm.

54 ENVIRONMENTAL SCIENCES↗

Implementation and Evaluation of Physics-Driven Dynamic Entrainment-Mixing Parameterization in a Climate Model and Its Impact on Low-Cloud Simulation

The turbulent entrainment-mixing process in the Community Earth System Model version 1.2 (CESM1.2) is assumed to follow the extremely inhomogeneous entrainment-mixing. However, different entrainment-mixing scenarios can occur in real clouds. To address this deficiency, a unifying parameterization that represents different entrainment-mixing processes is implemented and evaluated in CESM1.2. The results indicate that the homogeneous mixing degree values simulated by the new parameterization in CESM1.2 are predominantly greater than 50%, suggesting a tendency toward homogeneous mixing. Compared to the extremely inhomogeneous mixing mechanism, the new parameterization increases the cloud droplet number concentration (Nc). More importantly, the new parameterization improves low-cloud fraction (CLDLOW) simulation in Northwest Pacific (NWP) and Southeast Pacific (SEP) regions, with relative improvements of 2.95% and 4.17%, respectively. Furthermore, the improvements reach up to 44.6% and 16.2% in the NWP and SEP regions, respectively, when considering the relationship between N c and CLDLOW. Further analysis reveals that the new parameterization enhances cloud optical depth, longwave radiative cooling effect, net condensation rate, cloud water mixing ratio, lower-troposphere stability, and CLDLOW by increasing N c . Additionally, these results underscore the importance of improving entrainment-mixing parameterization in climate models.

54 ENVIRONMENTAL SCIENCES↗

The DOE E3SM version 2.1: overview and assessment of the impacts of parameterized ocean submesoscales

The U.S. Department of Energy's Energy Exascale Earth System Model (E3SM) version 2.1 builds on E3SMv2 with several changes, with the most notable being the addition of the Fox-Kemper et al. (2011) mixed-layer eddy parameterization. This parameterization captures the effect of finite-amplitude, mixed-layer eddies as an overturning streamfunction and has the primary function of restratification. Herein, we outline the changes to the mean climate state of E3SM that were introduced by the addition of this parameterization. Overall, the presence of the submesoscale parameterization improves the fidelity of the v2.1 simulation by reducing the ocean surface biases in the North Atlantic present in v2, as illustrated by changes in the climatological sea surface temperature and salinity and the Arctic sea-ice extent. Other impacts include a slight shoaling of the mixed-layer depths in the North Atlantic and a small improvement in the Atlantic Meridional Overturning Circulation (AMOC). We note that the expected shoaling due to the parameterization is regionally dependent in our coupled configuration. In addition, we investigate why the parameterization and its impacts on mixed-layer depth have little impact on the simulated AMOC: despite increased dense-water formation in the Norwegian Sea, only a small fraction of the water formed makes its way south into the North Atlantic basin. Version 2.1 also exhibits small improvements in the atmospheric climatology, with smaller biases in many notable quantities and modes of variability.

54 ENVIRONMENTAL SCIENCES↗

Parameterization of cloud transmittance for expeditious assessment and forecasting of all-sky DNI

Radiative transfer models require vast computing resources to solve cloud transmittance and reflectance from the radiative transfer equation. As a result, models offering precise simulation in operations often acquire individual cloud transmittance or reflectance from a lookup table precomputed for practicable scenarios. To further expedite the computation of global horizontal irradiance and to reduce the storage requirements, the Fast All-sky Radiation Model for Solar applications (FARMS) parameterized the lookup table using elementary functions with specified coefficients. This study extends FARMS direct normal irradiance (DNI) computation by utilizing hyperbolic tangent functions and various polynomial functions to parameterize the cloud transmittance for scattered solar radiation in the circumsolar region. The parameterization is implemented in FARMS with DNI (FARMS-DNI) and accounts for the circumsolar radiation when assessing or forecasting DNI. The evaluation, with long-term observations at the National Renewable Energy Laboratory's, Solar Radiation Research Laboratory, and the Atmospheric Radiation Measurement, Southern Great Plains, Central Facility, shows that the parameterized DNIs are virtually identical with those computed by coupling FARMS-DNI to a lookup table of cloud transmittance. This parameterization has diverse applications in radiative transfer models and numerical weather prediction models used to assess or forecast direct solar radiation.

14 SOLAR ENERGY↗

Mean field model parameterization to recover coverage-dependent kinetics

Lateral interactions between adsorbates introduce coverage dependence into adsorption energies and activation barriers of surface reactions. Lattice-based kinetic Monte Carlo (kMC) simulations can capture these interactions quantitatively but are laborious to parameterize and solve. Mean field models are more tractable, but protocols to construct and parameterize them are unclear. Here we explore the ability of a coverage-aware mean-field model to map to a lattice-kMC model of a generic two-step reaction network, including quasi-equilibrated adsorption and rate-limiting dissociation steps. We derive expressions for mean-field and coverage-dependent adsorption energies and dissociation barriers and parameterize against lattice-kMC predictions. We show that the parameterized mean-field rates correlate with ground truth lattice-kMC results across a wide range of reaction conditions and identify regions where the mean field fails. The mean field model similarly captures kMC-derived rate-order, Arrhenius and Sabatier plots at a greatly reduced computational cost. Further, the results provide guidance for parameterizing mean-field models, benchmarked against explicit lattice-based approaches for incorporating the influence of coverage effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗