Abstract Simulating atmospheric chemistry in Earth system models is critical for climate projections but remains computationally intensive. Comprehensive mechanisms, such as the MOZART‐T1 scheme in the Community Earth System Model (CESM), often limit the feasibility of long‐term or large‐ensemble simulations. We introduce and evaluate T4, a new simplified tropospheric chemistry mechanism (63 species, 135 reactions) designed as a high‐performance alternative to the standard T1 mechanism (151 species, 287 reactions). Using nudged (MERRA‐2) CESM simulations for the period 2003–2008, we performed a cross‐evaluation of both schemes against observational data sets, focusing on key climate‐relevant species: ozone (O 3 ), the hydroxyl radical (OH), and aerosols. The global mean tropospheric ozone column shows good agreement between the simulations, differing by less than 2%, while comparisons with ozonesonde data confirm that T4 robustly captures O 3 seasonal cycles and spatial distributions. Global tropospheric O 3 budgets and large‐scale distributions of aerosols and OH remain highly consistent between the two schemes. Furthermore, independent process‐level evaluations via box modeling confirm that T4 preserves the nonlinear sensitivities of the parent mechanism across diverse chemical regimes. While shared model biases exist, such as an underestimation of aerosol optical depth and a high‐OH bias, these are present in both simulations and are not artifacts of the T4 simplification. Ultimately, the T4 scheme achieves a ∼30% reduction in total computational cost while maintaining the scientific integrity of the complex T1 mechanism, providing a robust and efficient tool for multi‐century climate simulations and ensemble studies with CESM.
Abstract A novel methodology, using energy tracers, is introduced with the aim of diagnosing numerical energy dissipation, both globally and locally, in numerical models of the atmosphere. Energy dissipation might correspond to some physical process, such as the cascade of kinetic energy to unresolved scales if that energy is not restored as heat. Energy dissipation might also arise as an artifact of the numerical methods used; for example, in the current study the model used conservatively transports entropy, neglecting entropy sources due to mixing, resulting in a spurious energy loss. The energy tracer methodology is applied to Implicit Large Eddy Simulation of several canonical atmospheric boundary layer flows. The method is found to produce plausible local estimates of kinetic energy dissipation that are correlated with the local rate of strain. However, it does not yield useful estimates of the local spurious internal energy loss due to numerical mixing; possible reasons are discussed. The energy tracer method does produce useful estimates of the global kinetic energy dissipation and internal energy loss. For simple cases, the global internal energy loss estimates are confirmed by an independent method based on changes in the pdf of specific entropy or total specific humidity. The spurious global internal energy loss can be reduced by conservatively transporting, instead of entropy, a thermodynamic variable that is more nearly linearly mixing. This idea is analyzed theoretically, and is demonstrated in simulations that transport a quantity approximating the ice‐liquid water potential temperature.
Abstract Langmuir turbulence plays a critical role in the oceanic surface boundary layer by efficiently transporting momentum, heat, gases, and nutrients. Since its characteristic scale (meters to tens of meters) is far smaller than typical grid cells of ocean general circulation models, it must be parameterized. A key limitation of existing Langmuir schemes is the omission of Langmuir‐induced nonlocal fluxes. While these schemes reproduce scalar fields reasonably well, the lack of nonlocal momentum flux results in velocity simulations with excessive vertical shear and unrealistic near‐surface values. To overcome this limitation, we introduce an enhanced Langmuir turbulence parameterization that incorporates a unified formulation for both Langmuir and convective nonlocal fluxes of momentum and scalars into the K‐profile parameterization framework. When evaluated against large‐eddy simulation benchmarks, the new scheme demonstrates significant improvement in velocity simulations while maintaining excellent accuracy for scalar fields. These results underscore the necessity of including nonlocal fluxes for accurate modeling of Langmuir turbulence effects.
Abstract Fjords are a crucial connection between the Greenland Ice Sheet and the ocean, but remain unrepresented at the scale of many Earth System Models. To parameterize mixing within them, we modify a two‐layer estuary box model to include buoyant plumes, which are common features of glacial fjords. This fjord box model allows us to estimate primarily the salinity of the water mass exported to the open ocean. We compare high‐resolution MITgcm simulations and observations to both the fjord box model and results from buoyant plume theory. The volume transport out of the fjord is increased in the fjord box model compared to a buoyant plume alone. However, the volume of shelf water entrained into the buoyant plume is a key control on the properties of the water mass exported from the fjord into the open ocean. This model is also used to estimate the temperature of glacially modified water by using the temperature of the water mass entering the fjord as a tuning parameter. We find that the fjord box model could improve the salt flux into the ocean from fjords, but that temperature is highly sensitive to the effective temperature of the freshwater flux, which is based on a ratio of meltwater and subglacial discharge and is challenging to estimate.
Abstract Organic aerosols (OA) are a major component of fine particulate matter that affects air quality and climate, yet atmospheric models often underestimate their concentrations, partly reflecting uncertainties in the assumed volatility distribution of primary organic aerosol emissions. Using the NASA GISS ModelE Earth system model, we test four hypotheses: OA biases decrease when volatility distributions are differentiated by (H1) emission source, (H2) anthropogenic sector, (H3) geographic region, and (H4) VBS volatility bin. Simulations are evaluated against IMPROVE over the Continental US, ACTRIS over Europe, and the Chen et al. (2024, https://doi.org/10.1038/s41467‐024‐48902‐0) field‐campaign data set over China; for Africa and India, where direct OA observations are sparse, modeled OA is compared with MERRA‐2 reanalysis and complemented by MODIS/CALIPSO aerosol optical depth (AOD). Optimized volatility distributions reduce OA biases by up to 35% relative to the baseline, with optimal profiles varying across regions, seasons, and sectors. To extend these gains to data‐limited regions, we train Random Forest, XGBoost, and a back‐propagation neural network to construct spatiotemporally variable distributions. Although this improves performance, purely statistical predictions produce unrealistic summertime overestimations because they neglect the underlying chemistry. We therefore impose a physicochemical constraint based on RO2 + NO chemistry, activated where fNO exceeds a piecewise‐regression threshold, and anthropogenic plus biomass‐burning OA emissions exceed the monthly 75th percentile, which reduces biases by up to 77% in the most overestimated regions. Aerosol‐population diagnostics show that volatility changes redistribute organic mass among primary‐organic, black‐carbon–organic, and organic–sulfate populations, providing a physically consistent pathway for improving OA representation.
Abstract Numerical experimentation using an atmospheric configuration of the Goddard Earth Observing System (GEOS) Earth System Model is used to examine the vertical structure of the simulated Quasi‐Biennial Oscillation (QBO). Using an improved representation of the parameterized gravity wave spectrum, it is demonstrated that with sufficient vertical resolution (about 300–500 m grid spacing) in the lower stratosphere, the model can capture a QBO that extends all the way down to the tropical tropopause, in agreement with observations. The statistical characteristics of this simulated QBO closely resemble those of the observed oscillation, including the bimodal wind distribution, amplitude, mean period, and event‐to‐event variations. This substantial improvement over previous model simulations is attributed to both the careful tuning of the parameterized spectrum of traveling gravity waves and the enhanced vertical resolution in this version of the GEOS model.
Abstract Understanding what controls the horizontal scale of mesoscale cellular convection is central to explaining cloud self‐organization and its radiative impacts. Using a hierarchy of large‐eddy simulations, we investigate cell broadening in a well‐mixed boundary layer by isolating the roles of radiation, cloud microphysics, and water vapor. In cloudy simulations, cellular convection develops large aspect ratios (∼20–30) and forms donut‐like open cells with thick cloud walls, where open cells are defined dynamically based on the water‐vapor perturbation field. Even when radiative and microphysical effects are entirely removed, water vapor alone still self‐organizes into cellular structures with aspect ratios of ∼10. In these vapor‐only simulations, cell size is regulated primarily by surface sensible heat flux under the necessary condition of surface moisture supply, while remaining largely insensitive to the absolute magnitude and vertical distribution of water vapor. We identify mixing‐induced cooling across the entrainment interface layer (EIL) as the key mechanism enabling cell broadening without cloud‐related feedbacks. Within this idealized framework, we introduce Δ s l /Δ z i , the mean gradient of liquid water static energy across the EIL, as a post‐hoc and process‐oriented diagnostic to quantify the relative strength of mixing‐induced cooling across the EIL. Composite stream‐function analysis reveal qualitatively similar mesoscale overturning circulations in cloudy and vapor‐only simulations, highlighting the role of cooling effects across the EIL in cellular organization. These results reveal a pathway for cell broadening in water‐vapor‐only conditions and underscore the need for future work on the nonlinear interplay among mixing, radiation, and microphysics in regulating mesoscale cellular organization.
Abstract Disturbances profoundly impact forest capacity for sequestering and storing carbon, and the recovery rates after disturbances vary geographically. Many terrestrial carbon models inadequately simulate the effects of forest disturbances on biomass due to their reliance on equilibrium assumptions, the absence of historical disturbance data, as well as homogeneous vegetation parameters. In this study, we developed a new hybrid machine learning framework to optimize the spatial distribution of the parameters of a process‐based model, the integrated biosphere simulator (IBIS), across global forest regions. High‐resolution satellite‐derived products of gross primary productivity (GPP), leaf area index (LAI), forest age, and biomass were used as references to optimize parameters of both fast and slow carbon processes in the IBIS model. By integrating age maps and spatially explicit growth curves for biomass accumulation, our model was able to better represent the biomass dynamics in regenerating forests after disturbances. Our findings underscored the role of spatially optimized parameters in accurately simulating GPP, LAI, and biomass across global forests, with particular gains from accounting for age structures. The optimized IBIS model shows superior performance in reproducing biomass gradients across climate zones, compared with global satellite‐derived products and simulations from multiple dynamic global vegetation models (DGVMs). The optimization revealed a greater carbon sequestration potential in regrowing forests after disturbances. Our framework provides a new strategy for using forest age data to improve the accuracy of large‐scale forest carbon simulations in DGVMs.
Abstract Stable water isotopes serve as tracers of climate processes and are useful for identifying drivers of regional and global hydrological variability. To get a precise picture of spatiotemporal changes in the water cycle, it is necessary to describe the mechanisms in a coherent way among the involved climatic reservoirs (atmosphere, land, and ocean). For example, in the Pacific Ocean, the oxygen isotopic composition (denoted δ 18 O) of surface seawater recorded in corals is widely used to reconstruct the El Niño–Southern Oscillation (ENSO). However, the influences of atmosphere–ocean feedback and ocean circulation on the δ 18 O–ENSO relationship are not fully understood. Describing water isotopes in the full climate system is one way to tackle this issue. Therefore, this study introduces the fully coupled isotopic version of the Model for Interdisciplinary Research on Climate version 6 (MIROC6‐iso). MIROC6‐iso exhibits good performance in reproducing spatial isotopic variations in precipitation, water vapor, and ocean water, and the relationships of δ 18 O with temperature and salinity against observations. We also find that the atmosphere‐ocean Coupled General Circulation Model (CGCM) captures δ 18 O sw (seawater) variations significantly better than a configuration where an Atmospheric General Circulation Model is coupled to a 1D slab ocean model in Pacific Ocean in climatological condition and different ENSO phases. Budget analysis indicates that the better performance of the CGCM configuration is due to fully resolved oceanic vertical mixing and horizontal advection. This study shows that MIROC6‐iso is useful to reconstruct past climate changes and examine the recent changes in the water cycle.
Abstract Direct in situ measurements of sea surface currents (SSC) at submesoscales (1–100 km) are challenging. For this reason, inversion techniques have been utilized to infer SSC from satellite sea surface temperature (SST) data, which are straightforward to obtain. However, existing inversion methods often do not adequately account for uncertainty. Here, we present a physics‐based statistical inversion model to predict submesoscale SSC at a high‐temporal resolution using hourly remotely sensed SST data. Our approach employs Gaussian process (GP) regression that is informed by a two‐dimensional tracer transport equation. Our method yields a predictive distribution of SSC, from which we can generate an ensemble of SSC to construct both predictions and prediction intervals. Our approach incorporates prior knowledge of the SSC length scales and variances elicited from a numerical model; these are subsequently refined using the SST data. The framework naturally handles noisy and spatially irregular SST data (e.g., due to cloud cover), without the need for pre‐filtering. We validate our inversion method through an observing system simulation experiment, which demonstrates that GP‐based statistical inversion outperforms the existing global optimal solution method, especially when the measurement signal‐to‐noise ratio is low. When applied to Himawari‐9 satellite SST data over the eastern Indian Ocean, our method successfully resolves SSC down to the submesoscale. We anticipate our framework will be used to improve understanding of fine‐scale ocean dynamics, and to facilitate the coherent propagation of uncertainty into downstream applications such as ocean particle tracking.
Abstract Accurate and comprehensive representation of aerosols in Earth system models (ESMs) is critical for modeling radiative forcing and seasonal‐to‐decadal variability. With increasing computing power, detailed physical and chemical processes representing aerosols and their interactions with other components of the Earth system can be treated more explicitly and accurately in ESMs. Like many other ESMs, the U.S. DOE Energy Exascale Earth System Model (E3SM) versions 1 and 2 have a state‐of‐the‐art treatment of major aerosol species but crudely treat or even neglect some aerosol components that become increasingly important in the future with decreasing sulfur emissions. Several science‐driven model developments of new aerosol features, including an explicit treatment of nitrate and ammonium aerosol species using MOSAIC coupled with the chemUCI gas chemistry scheme, explicit secondary organic aerosol (SOA) formation and loss, prognostic stratospheric sulfate (using chemical, microphysical and optical treatments instead of prescribing optical properties for volcanic aerosol), improved convective wet removal, improved numerical coupling of aerosol processes (i.e., emission, dry deposition, and turbulent mixing), and a new dust particle emission scheme, have been included in E3SM version 3 (E3SMv3) to better capture their roles in the Earth system. These new aerosol developments also require coupling with relatively comprehensive atmospheric chemistry to represent the reactions involving precursor gases and oxidants. Besides the new modeling capabilities, the aerosol improvements (e.g., SOA and dust lifetime and spatial distribution) contribute to E3SMv3's better performance in reproducing the historical temperature trends and enable the model to better project near‐future Earth system changes.
Abstract Large‐eddy simulations (LES) are commonly employed to study small‐scale weather phenomena and to validate coarser models. Like larger‐scale weather and climate models, they contain weakly constrained parameters and use physical inputs with associated uncertainties, such as initial conditions or forcing. This study assesses the viability of the ensemble Kalman smoother (EnKS) to tune both parameters and physical inputs of an LES simulation towards campaign measurements. The EnKS relies on a perturbed parameter ensemble, as is common in sensitivity analysis. By returning an updated ensemble over the tuning parameters, it provides optimal values together with uncertainty estimates. In a Bayesian sense, it balances parametric and measurement uncertainties objectively. The methodological simplicity enables an in‐depth interpretation of both model sensitivities and the calibration results. The methodology is demonstrated by calibrating the PyCLES model towards measurements of nocturnal marine stratocumulus clouds (DYCOMS‐II RF01) at a horizontal resolution of 35 m. Using a WENO finite volume scheme for advection, the model with calibrated inputs improves over models compared in Stevens et al. (2005, https://doi.org/10.1175/mwr2930.1 ), indicating that errors in the prescribed initial condition and forcing may have contributed to biases shared by most tested LES models. The repetition of the calibration with two numerical advection schemes highlights that parametric calibration can only reach a satisfying performance of the improved simulation for models that are not dominated by structural errors. The presented methodology provides a transparent and interpretable framework for model calibration using observations with quantified uncertainties.
Abstract The upper boundary condition treatment in atmospheric models has a pronounced impact on stability and performance. At the same time, the choice of damping settings can severely impact atmospheric states by not sufficiently preventing back‐reflections of vertically propagating waves from the model top or provoking back‐reflections from the damping layer. A particular challenge is the broad spectrum of upward propagating waves, with horizontal wavelengths between 10 and 10,000 km. In the Icosahedral Nonhydrostatic Weather and Climate Model (ICON), the numerical formulation includes a Klemp Rayleigh damping acting on the vertical velocity in higher atmospheric levels. However, Klemp Rayleigh damping does not yield a uniform damping efficiency over the horizontal wavelength spectrum. This necessitates overdamping of short wavelengths to sufficiently damp the long wavelengths, risking the introduction of artificial back‐reflection from the damping layer. In this work, an extended formulation of the upper‐level wave absorber is proposed that yields a more uniform attenuation of vertically propagating waves across the wave spectrum by introducing vertical diffusion damping on horizontal velocities. This damping scheme explicitly targets the challenges encountered in km‐scale simulations where an increasing number of wavelengths have to be accounted for. Global 10‐km resolution ICON simulations are conducted to investigate the suitability of the proposed upper‐level damping scheme. The results demonstrate improved simulation stability and more efficient damping of long waves. The representation of the mean atmospheric circulation and surface climate remains largely unchanged.
Abstract In global subseasonal forecasting using dynamical models, correcting the systematic biases of Madden–Julian Oscillation (MJO) predictions has proven critical, particularly due to issues of rapid amplitude damping and phase distortion. To address these biases, recent studies have demonstrated that deep learning offers a promising solution by learning mappings that directly translate biased dynamical model outputs to ground truth MJO indices, effectively serving as post‐processing bias correctors. These approaches implicitly assume that a single neural network can extract all relevant features necessary for bias correction across different forecast time steps. However, we observe that the relationships between forecast lead times and their corresponding corrections are more intricate: features relevant to short range forecasting error differ significantly from those that govern long range forecasting errors. Consequently, direct mapping strategies often result in suboptimal performance, excelling in either short or long range forecasts, but rarely both. To address this challenge, we propose a unified attention recurrent neural network framework that processes the full sequence of dynamical forecasts using a masked input tensor, enabling the model to extract temporally contextualized features across all lead times. Additionally, we introduce a phase regulated loss function that explicitly penalizes errors in both amplitude and phase, capturing the cyclical structure of MJO more effectively than traditional mean squared error based objectives. Comprehensive evaluations on operational subseasonal to seasonal reforecast data sets demonstrate that our method significantly improves forecast accuracy and lead‐time consistency.
Abstract During the past decades, the rapid decline of sea ice in the Arctic Ocean has substantially favored commercial navigation activities in the summertime. Numerical sea ice prediction on a seasonal scale plays a crucial role in guiding the programme of such activities, yet the role of snow depth data assimilation in numerical sea ice prediction has not been clearly addressed in previous studies. With the aid of a coupled Arctic sea ice‒ocean‒atmosphere modeling system, two sets of runs have been conducted: one assimilates sea ice concentration, sea ice thickness, and sea surface temperature in the ice‐free region; the other one also assimilates snow depth overlying the ice synchronously. We have found that driven by perfect boundary conditions, wintertime snow depth assimilation generally has a positive effect on the September sea ice prediction initialized in early June, and the positive effect gradually weakens along with the delay of prediction onset from early June to early August. The effect has an intimate relationship with the changes in sea ice thickness and snow depth in the model state at the prediction onset, which eventually affects September sea ice prediction in the coupled system via model physics.
Abstract High‐latitude clouds, present over the Arctic Ocean, the Southern Ocean and the Antarctic continent, are very often mixed‐phase clouds (MPCs), that is, composed of both supercooled liquid droplets and ice crystals. Despite being essential for the climate of the poles, they remain a major modeling challenge for climate models. In this study, we present a new cloud phase partitioning parameterization developed for the LMDZ atmospheric model. This parameterization is based on the theory of the evolution of supersaturation in a turbulent environment and is inspired by previous theoretical and modeling works. This scheme completely abandons the standard temperature dependent phase partitioning used in the model to predict the amount of supercooled liquid water in clouds as a function of turbulent kinetic energy, resolved vertical velocity and pre‐existing ice crystal properties. This new scheme is evaluated over the Southern Ocean with observation from the MARCUS campaign and results show an improvement in the simulation of the cloud phase spatial variability. The sensitivity to the crystal number concentration, determined by a prescribed concentration of ice nucleating particles, is also assessed. A second evaluation is performed in the Arctic region with observations collected in mid‐level frontal clouds during the RALI‐Thinice campaign and a perturbed parameter ensemble experiment is conducted to assess the parametric sensitivity. The new scheme suppresses the systematic overestimation of liquid far from cloud top and shows the ability to simulate patches and thin layers of supercooled liquid water as commonly observed in polar frontal clouds.
Abstract Coupled data assimilation (CDA) could be beneficial for paleoclimate reconstruction, but intermediate‐complexity climate models are often used. The deep learning (DL)‐based surrogate model that can realistically simulate the climate system provides alternative to CDA, so that CDA of multi‐timescale proxy data using DL‐based models is investigated for paleoclimate reconstruction. Results reveal that at the annual time scale, coupling an oceanic component to the atmospheric model is beneficial for the surface air temperature (SAT) forecasts, but coupling an atmospheric component to the oceanic model slightly degrades the sea surface temperature (SST) forecasts, since coupling the atmospheric component introduces high frequent noises to the oceanic model. Compared to the coupled model component, cross‐component update by assimilating cross‐component proxy data has larger positive impacts on SAT and SST reconstructions. Moreover, simultaneously assimilating atmospheric and oceanic proxy data with a coupled model yields the most accurate SAT and SST reconstructions.
Abstract Mesoscale eddies are the dominant reservoir of kinetic energy (KE) in the ocean and a key component of the Earth's climate system. Current state‐of‐the‐art climate models can only partially resolve mesoscale processes due to the limited spatial resolution imposed by computational resources, making the accurate parameterization of unresolved KE transfers crucial. In recent years, a growing number of studies use machine learning tools to build data‐driven eddy parameterizations. In this work, we implement two such parameterizations, Zanna and Bolton (2020, https://doi.org/10.1029/2020gl088376) (ZB20) and Guillaumin and Zanna (2021, https://doi.org/10.1029/2021ms002534) (GZ21), into the Nucleus for European Modeling of the Ocean (NEMO) ocean model. We tune and evaluate them against a higher‐resolution ground truth, and compare them to a baseline backscatter parameterization in an idealized Atlantic basin configuration. GZ21 is unaware of the model grid, resulting in a systematic bias in the predicted fluxes tied to the local grid spacing. It does not improve the coarse simulation concerning any metrics presented here. ZB20 accurately predicts subgrid fluxes and improves both local KE spectra and large‐scale circulation. It yields an improved mean state comparable to that of the baseline parameterization, consistent with previous studies. We emphasize the importance of carefully designed training data, which takes into account all resolution‐dependent model components, such as viscosity and model geometry. Our findings provide guidance for the future development of robust and generalizable data‐driven eddy parameterizations.
Abstract The ultraviolet (UV) and visible spectral regions account for about half of the solar incoming energy, making the accurate treatment of ozone, oxygen and water vapor and Rayleigh scattering in this region crucial for understanding solar radiation modulation through absorption and scattering. The absorption/scattering coefficients for ozone, oxygen and Rayleigh exhibit smooth spectral features, enabling a sub‐band approach that preserves critical spectral details, such as UVA, UVB, UVC bands, and photo synthetically active radiation (PAR). An optics–radiative‐source correlation principle is proposed, which requires that spectral mapping preserve the local correlation between gaseous optical properties and the solar source. Enforcing this constraint yields band‐mean coefficients that are uniquely determined and robust, whether formulated in frequency space or in cumulative‐probability space. This study clarifies the fundamental physics underlying gaseous transmission and Rayleigh scattering, showing that parameterizations can be derived by accounting for the spectral variability of absorption and scattering coefficients, as well as their correlation with incoming solar energy. The proposed physical principles can eliminate the need for manual interventions and naturally produce accurate results for gaseous transmission and Rayleigh scattering, achieving maximum computational efficiency by requiring a very limited number of radiative transfer calculations. Furthermore, the sub‐band approach enables precise UV index predictions in operational weather forecasting models, constituting a novel contribution for the modeling community.
Abstract We present the implementation of an inline three‐dimensional (3D) turbulent kinetic energy (TKE)‐based subgrid diffusion scheme in the Geophysical Fluid Dynamics Laboratory (GFDL) Finite‐Volume Cubed‐Sphere (FV3) dynamical core. This scheme addresses the need for a unified and physically grounded treatment of turbulence as FV3 is increasingly used across the gray zone and large‐eddy simulation scales. Building on the 3D TKE framework introduced in Zhu et al. (2025, https://doi.org/10.1038/s41612‐025‐01117‐6), we embed the full TKE budget calculations, including the 3D shear production, and TKE‐informed horizontal and vertical diffusion directly into the FV3 core. Key features include computation of 3D TKE shear production based on FV3 D‐grid winds, updating of TKE and diffusion coefficients within FV3 time‐stepping loop, and extension of TKE‐based horizontal diffusion to all dynamical quantities. This integration avoids reliance on external physics packages and improves consistency between resolved and subgrid processes. The inline 3D TKE scheme offers a robust alternative to numerical damping in FV3 and enables a physically based representation of 3D subgrid‐scale diffusion that is well suited for applications at grid spacings of ∼100 m and finer.
