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At least 109 records · Page 6

Visualizing an Exascale Data Center Digital Twin: Considerations, Challenges and Opportunities

Digital twins are an excellent tool to model, visualize, and simulate complex systems, to understand and optimize their operation. In this work, we present the technical challenges of real-time visualization of a digital twin of the Frontier supercomputer.We show the initial prototype and current state of the twin and highlight technical design challenges of visualizing such a large High Performance Computing (HPC) system. The goal is to understand the use of augmented reality as a primary way to extract information and collaborate on digital twins of complex systems. This leverages the spatio-temporal aspect of a 3D representation of a digital twin, with the ability to view historical and real-time telemetry, triggering simulations of a system state and viewing the results, which can be augmented via dashboards for details. Finally, we discuss considerations and opportunities for augmented reality of digital twins of large-scale, parallel computers.

Maiterth, Matthias↗

Disentangling the chemistry and transport impacts of the quasi-biennial oscillation on stratospheric ozone

The quasi-biennial oscillation (QBO) in tropical winds perturbs stratospheric ozone throughout much of the atmosphere via changes in transport of ozone and other trace gases, as well as via temperature changes, both of which alter ozone chemistry. Attributing these causes of QBO–ozone variability may provide insights into model-to-model differences that contribute to ozone simulation. Here we develop a novel metric of steady-state ozone (SSO) to separate these effects: SSO calculates the local steady-state response of ozone due to the changes in temperature, chemical species, and overhead ozone column; the response due to circulation change is presumed when SSO shows no response. It is applied to the nudged Department of Energy's Energy Exascale Earth System Model version 2 (E3SMv2) with interactive ozone chemistry to demonstrate its validity. The E3SMv2 simulations nudged to reanalysis data produced reasonable wind and ozone patterns, especially in the tropics. Consistent with previous studies, we find clear demarcations with pressure. Ozone perturbations in the upper stratosphere (<6 hPa) are predicted by temperature changes; those between 6 and 20 hPa are predicted by NO y changes, and those in the lower stratosphere show no temperature or NO y response and are presumably driven by circulation changes. These results are important for diagnosing model-to-model discrepancy in QBO–ozone response and enhancing the reliability of ozone projections.

Xie, Jinbo [Lawrence Livermore National Laboratory↗

Multiscale Nuclear-Electronic Orbital Quantum Dynamics in Complex Environments

Many renewable energy conversion processes rely on the movement of protons as well as electrons through either electrocatalysis or photoexcitation. The simulation of such processes requires a quantum mechanical description of coupled nuclear-electronic dynamics in a solvent or heterogeneous chemical environment. The overall objective of this project is the development of theoretical and computational capabilities for simulating nuclear-electronic quantum dynamics in complex environments and the creation of high-performance, open-source software. This multiscale framework will enable simulations of the real-time dynamics of nonequilibrium excited state proton-coupled electron transfer, quantum decoherence, vibronic energy transfer, and ultrafast radiolysis, as well as their associated time-resolved multidimensional spectroscopies. An important outcome of this project will be a sustainable, reusable, and interoperable open-source software ecosystem. This software will be designed for emerging exascale and future national leadership computers. Another key outcome will be a multiscale quantum dynamics method and software enabling simulations of nonequilibrium nuclear-electronic quantum dynamics in complex environments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Validating a microphysical prognostic stratospheric aerosol implementation in E3SMv2 using observations after the Mount Pinatubo eruption

Abstract. This paper describes the addition of a stratospheric prognostic aerosol (SPA) capability – developed with the goal of accurately simulating sulfate aerosol formation and evolution in the stratosphere – in the Department of Energy (DOE) Energy Exascale Earth System Model, version 2 (E3SMv2). The implementation includes changes to the four-mode Modal Aerosol Module microphysics in the stratosphere to allow for larger particle growth and more accurate stratospheric aerosol lifetime following the Pinatubo eruption. E3SMv2-SPA reasonably reproduces stratospheric aerosol lifetime, burden, aerosol optical depth, and top-of-atmosphere flux when compared to remote sensing observations. E3SMv2-SPA also has close agreement with the interactive chemistry–climate model CESM2-WACCM (Community Earth System Model version 2–Whole Atmosphere Community Climate Model) – which has a more complete chemical treatment – and the observationally constrained, prescribed volcanic aerosol treatment in E3SMv2. Global stratospheric aerosol size distributions identify the nucleation and growth of sulfate aerosol from volcanically injected SO2 from both major and minor volcanic eruptions from 1991 to 1993. The modeled aerosol effective radius is consistently lower than satellite and in situ measurements (max differences of ∼ 30 %). Comparisons with in situ size distribution samples indicate that this simulated underestimation in both E3SMv2-SPA and CESM2-WACCM is due to overly small accumulation and coarse-mode aerosols 6–18 months post-eruption, with E3SMv2-SPA simulating ∼ 50 % of the coarse-mode geometric mean diameters of observations 11 months post-eruption. Effective radii from the models and observations are used to calculate offline scattering and absorption efficiencies to explore the implications of smaller simulated aerosol size for the Pinatubo climate impacts. Scattering efficiencies at wavelengths of peak solar irradiance (∼ 0.5 µm) are 10 %–80 % higher for daily samples in models relative to observations through 1993, suggesting higher diffuse radiation at the surface and a larger cooling effect in the models due to the smaller simulated aerosol; absorption efficiencies at the peak wavelengths of outgoing terrestrial radiation (∼ 10 µm) are 15 %–40 % lower for daily samples in models relative to observations, suggesting an underestimation in stratospheric heating in the models due to the smaller simulated aerosol. These potential biases are based on aerosol size alone and do not take into account differences in the aerosol number. The overall agreement of E3SMv2-SPA with observations and its similar performance to the well-validated CESM2-WACCM makes E3SMv2-SPA a viable alternative to simulating climate impacts from stratospheric sulfate aerosols.

Brown, Hunter York (ORCID:0000000218147874)↗

Understanding Biases in Simulated Cloud Radiative Effects in E3SMv3

This study systematically investigates biases in cloud radiative effects (CREs) within the recently released Energy Exascale Earth System Model version 3 (E3SMv3). Compared to its previous version (E3SMv2), E3SMv3 shows excessively strong shortwave CRE over tropical and subtropical oceans, the Southern Ocean, and the Northern Hemisphere storm tracks, which is primarily caused by an overestimation of optically intermediate low clouds. The model also displays excessive longwave CRE over the Maritime Continent and other tropical deep convection regions, resulting from an overestimation of optically thick high clouds. Implementing the Predicted Particle Properties (P3) scheme for stratiform clouds played the most significant role in these cloud changes. In addition, using a double-moment scheme for convective clouds contributed to the increase in intermediate low clouds and optically thick clouds in tropical deep convection regions. Error metrics for total cloud amount (E TCA ), cloud properties (E ctp-τ ), and cloud properties weighted by their SW and LW radiative impacts (E SW and E LW ) indicate that E3SMv3's ability to reproduce observed cloud radiative effect of low, middle, and high clouds has not been improved compared to E3SMv2. Nevertheless, the performance of E3SMv3 remains well within the spread of CMIP6 models, with E SW and E LW values smaller than those in most CMIP6 models. This study underscores the importance of integrating diverse satellite observations for robust cloud evaluation and using cloud-radiation relationships as consistency check for model errors. It suggests that further model developments focus on improving cloud microphysics and their interactions with radiation.

Environmental sciences↗

Influence of Antarctic and Greenland Continental Shelf Circulation on High‐Latitude Oceans in E3SM

The science objectives of this project are to simulate and understand the impacts of both deep-basin warm-water intrusions and land-ice melt on the continental shelf circulations and sea-ice distributions around the margins of Greenland and Antarctica. As well, the role of subsurface ocean heat from the Atlantic on declining sea-ice cover in the Arctic is explored. Mesoscale processes and fine bathymetry are implicated in cross-shelf property transports around both Greenland and Antarctica. Therefore, we configured and ran an atmospheric reanalysis-forced global ocean/sea-ice simulation on a grid that reduces from 8 km at the Equator to 2 km at the poles (UH8to2) with 60 vertical levels. It was produced using the Energy Exascale Earth System Model ‘‘HiLAT’’ code (E3SMv0-HiLAT) that uses the Parallel Ocean Program (POP) and CICE5 as its ocean and sea-ice components, respectively. Two main UH8to2 simulations were carried out: one for 1975-2009 and the other for July 2016-2020 after it was initialized from a 1/25° data-assimilative ocean/sea-ice prediction system ocean/sea-ice state. The UH8to2 is not coupled to an active land-ice model. Rather, land-ice melt is represented by observationally informed freshwater fluxes (FWFs). Short (multi-year) UH8to2 simulations were conducted to understand sensitivities when Greenland ice sheet (GrIS) melt is released only at the ocean surface or when it is distributed over the upper water column in accordance with fjord melt plume behavior; these cases were compared with a no GrIS melt case. West Greenland continental shelf currents were fastest in the vertical distribution case and an increase in baroclinic conversion at the shelf break associated with increased eddy kinetic energy was found relative to the surface release case. Further, salinity is lower and meltwater volume greater in the eastern Labrador Sea in the vertical distribution case. For the Arctic, the veracity of the UH8to2 was evaluated for 2017-2020 using available observations. Simulated seasonal sea-ice thickness and concentration are realistic, but the ice is unrealistically thin in the central and eastern Arctic in the fall. Comparisons of vertical sections of ocean temperature, salinity, and buoyancy collected from Ice-Tethered Profilers (ITPs) in the eastern Arctic in the fall and winter of 2019/2020 and co-located/concurrent UH8to2 fields show the stratification over the top 100 m of the water column is too low in the model, the simulated mixed layer too deep, and the simulated subsurface Atlantic Water (AW) too warm; these biases may contribute to the sea-ice biases. A model intercomparison study using the UH8to2 and a forced 1/25° regional Arctic ocean/sea-ice (uses the HYbrid Coordinate Ocean Model and CICE5) simulation further investigates the relationship between AW and sea-ice in the eastern Arctic. The models show a mesoscale-rich pulse of Atlantic Water extending into the eastern basin that reaches maximum intensity in late winter of 2018, after which it decreases in strength. Concurrent and co-located sea-ice melt or the inhibition of sea-ice growth is seen and is attributed to halocline mesoscale eddies doming into the mixed layer with convection bringing this heat into the vicinity of the sea-ice.

58 GEOSCIENCES↗

Observationally constrained analysis on the distribution of fine- and coarse-mode nitrate in global models

Nitrate plays an important role in the Earth system and air quality. A key challenge in simulating the life cycle of nitrate aerosol in global models is to accurately represent mass size distribution of nitrate aerosol. In this study, we evaluate the performance of the Energy Exascale Earth System Model version 2 (E3SMv2) and the Community Earth System Model version 2 (CESM2), along with Aerosol Comparisons between Observations and Models (AeroCom) phase III models, in simulating spatial distribution of fine-mode nitrate, the mass size distribution of fine- and coarse-mode nitrate, and the gas–aerosol partitioning between nitric acid gas and nitrate, using long-term ground-based observations and measurements from multiple aircraft campaigns. We find that most models underestimate the annual mean PM 2.5 (particulate matter with diameter less than 2.5 µm) nitrate surface concentration averaged over all sites. The observed nitrate PM 2.5 / PM 10 and PM 1 / PM 4 ratios are influenced by the relative contribution of fine sulfate or organic particles and coarse dust or sea salt particles. Overall, the ground-based observations give an annual mean surface nitrate PM 2.5 / PM 10 ratio of 0.7. Most models underestimate the annual mean PM 2.5 / PM 10 ratio in all regions. There are large spreads in the modeled nitrate PM 1 / PM 4 ratios, which span the full range from 0 to 1. Most models underestimate the surface molar ratio of nitrate to total inorganic nitrate averaged across all sites. Our study indicates the importance of gas–aerosol partition parameterization and the simulation of dust and sea salt in correctly simulating the mass size distribution of nitrate.

Nitrate↗

Evaluation of Flow Routing on the Unstructured Voronoi Meshes in Earth System Modeling

Flow routing is a fundamental process of Earth System Models' (ESMs) river component. Traditional flow routing models rely on Cartesian rectangular meshes, which exhibit limitations, particularly when coupled with unstructured mesh-based ocean components. They also lack the support for regionally refined models. While previous studies have highlighted the potential benefits of unstructured meshes for flow routing, their widespread application and comprehensive evaluation within ESMs remain limited. This study extends the river component of the Energy Exascale Earth System Model to unstructured Voronoi meshes. We evaluated the model's performance in simulating river discharge and water depth across three watersheds spanning the Arctic, temperate, and tropical regions. The results show that while providing several benefits, unstructured mesh-based flow routing can achieve comparable performance to structured mesh-based routing, and their difference is often less than 10%. Although the unstructured mesh-based method could address several existing limitations, this research also shows that additional improvements in the numerical method are needed to fully exploit the advantages of unstructured mesh for hydrologic and ESMs.

54 ENVIRONMENTAL SCIENCES↗

Origin of large variations of current on/off ratio and switching voltage in atomically thin memristors: an exascale ab initio transport study

Nonvolatile resistive switching in two-dimensional monolayers opens a new avenue for high-density memory/computing devices. However, questions remain as to why the current on/off ratio and switching voltage vary significantly among different devices. Here, we simulate electronic transport of large systems consisting of a h-BN monolayer sandwiched by gold electrodes, enabled by an implementation of the nonequilibrium Green’s function method in the exascale density functional theory (DFT) code: Real-space MultiGrid. Systematic calculations reveal that the wide range of on/off ratios is due to variations in interface distances between the electrode and h-BN that significantly modulate their wavefunction overlap. In addition, DFT calculations demonstrate that the energy barrier of a gold atom dissociating from the electrode to h-BN increases dramatically with the interface distance, thereby explaining the strong dependence of the switching voltage on distance. Our work demonstrates the significance of interface distance in governing the current on/off ratio and switching voltage.

Electronic devices↗

Enhancing Photosynthesis Simulation Performance in ESMs with Machine Learning-Assisted Solvers

When simulating vegetation dynamics, photosynthesis accounts for a large fraction of the computational cost in most Earth System Models (ESMs). This is largely since photosynthesis is represented as a system of nonlinear equations, and the solution requires the use of an initial guess followed by many iterations of the numerical solver to obtain a solution. We use machine learning (ML) to replicate the response surface of the model’s numerical solver to improve the choice of initial guess, therefore requiring fewer iterations to obtain a final solution. We implemented this test on the leaf-level calculations as well as at the canopy scale, and for both we observed fewer iterations of the photosynthesis solver when a ML-based initial guess was implemented. The model tested here is the Energy Exascale Earth System Model - Land Model (ELM). The ML-based algorithms used here are trained on simulations from the model itself and used only to improve the initial guess for the solver; therefore, the model maintains its own set of physics to obtain the final solution. This work shows novel ways to utilize ML-based methods to improve the performance of numerical solvers in ESMs.

Massoud, Elias [ORNL] (ORCID:0000000217725361)↗

Asynchronous-many-task systems: Challenges and opportunities - Scaling an AMR astrophysics code on exascale machines using Kokkos and HPX

Dynamic and adaptive mesh refinement is pivotal in high-resolution, multi-physics, multi-model simulations, necessitating precise physics resolution in localized areas across expansive domains. Today’s supercomputers’ extreme heterogeneity presents a significant challenge for dynamically adaptive codes, highlighting the importance of achieving performance portability at scale. Our research focuses on astrophysical simulations, particularly stellar mergers, to elucidate early universe dynamics. Here, we present Octo-Tiger, leveraging Kokkos, HPX, and SIMD for portable performance at scale in complex, massively parallel adaptive multi-physics simulations. Octo-Tiger supports diverse processors, accelerators, and network backends. Experiments demonstrate exceptional scalability across several heterogeneous supercomputers including Perlmutter, Frontier, and Fugaku, encompassing major GPU architectures and x86, ARM, and RISC-V CPUs. Parallel efficiency of 47.59% (110,080 cores and 6880 hybrid A100 GPUs) on a full-system run on Perlmutter (26% HPCG peak performance) and 51.37% (using 32,768 cores and 2048 MI250X) on Frontier are achieved.

97 MATHEMATICS AND COMPUTING↗

Exascale workflow applications and middleware: An ExaWorks retrospective

Exascale computers offer transformative capabilities to combine data-driven and learning-based approaches with traditional simulation applications to accelerate scientific discovery and insight. However, these software combinations and integrations are difficult to achieve due to the challenges of coordinating and deploying heterogeneous software components on diverse and massive platforms. Here, we present the ExaWorks project, which addresses many of these challenges. We developed a workflow Software Development Toolkit (SDK), a curated collection of workflow technologies that can be composed and interoperated through a common interface, engineered following current best practices, and specifically designed to work on HPC platforms. ExaWorks also developed PSI/J, a job management abstraction API, to simplify the construction of portable software components and applications that can be used over various HPC schedulers. The PSI/J API is a minimal interface for submitting and monitoring jobs and their execution state across multiple and commonly used HPC schedulers. We also describe several leading and innovative workflow examples of ExaWorks tools used on DOE leadership platforms. Furthermore, we discuss how our project is working with the workflow community, large computing facilities, and HPC platform vendors to address the requirements of workflows sustainably at the exascale.

97 MATHEMATICS AND COMPUTING↗

Assessment of Storm-Associated Precipitation and Its Extremes Using Observational Data Sets and Climate Model Short-Range Hindcasts

Heavy precipitation, often associated with weather phenomena such as tropical cyclones, extratropical cyclones (ETCs), atmospheric rivers (ARs), and mesoscale convective systems (MCSs), can cause significant socio-economic loss. Here, in this study, we apply atmospheric feature trackers to quantify the contributions of these storm types in observational data sets and climate model short-range hindcasts. We generate a global hourly storm data set at 0.25° spatial resolution covering 2006–2020, based on the tracking results from TempestExtremes and Python FLEXible object TRacKeR. Our analyses show that these four storm types account for 67% of global annual mean precipitation and 82% of top 1% precipitation extremes, with MCSs mainly over the tropics, and ARs and ETCs over the midlatitudes. The percentage of precipitation contributions from these storms also show strong seasonality over many geographical locations. We further apply the tracking results to the Energy Exascale Earth System Model (E3SM) short-range hindcasts and evaluate how well these storms are simulated. The evaluation show that E3SM, with ∼1° resolution, significantly underestimates storm-associated precipitation totals and extremes, especially for MCSs in the tropics. Our analysis also suggests that model fails to capture the correct mean diurnal phases and amplitude of MCS precipitation. This phenomenon-based approach provides a better understanding of precipitation characteristics and can lead to enhanced model evaluation by revealing underlying problems in model physics related to precipitation processes associated with the heavy-precipitating storms.

54 ENVIRONMENTAL SCIENCES↗

ELM‐MOSART‐DOC: A Large‐Scale Riverine Dissolved Organic Carbon Model and Its Application Over the United States

Riverine dissolved organic carbon (DOC), primarily sourced from soil organic carbon (SOC), plays a crucial role in regional and global carbon cycles. However, the complexities of the underlying mechanisms and limited observations present significant challenges for predictive understanding of DOC at regional or larger scales. Recently, we developed a machine learning‐based (ML) map of DOC transformation rates, bridging the gap between SOC and DOC leaching flux and simplifying terrestrial DOC representation. Building on this advancement, we introduce ELM‐MOSART‐DOC, a DOC module integrated into the riverine component of the Energy Exascale Earth System Model (E3SM)—the Model for Scale Adaptive River Transport (MOSART). ELM‐MOSART‐DOC simulates DOC transport and transformation across both headwater streams and river networks, including those managed. Model validation demonstrates the ability of ELM‐MOSART‐DOC to accurately capture long‐term average DOC concentrations, with Kling‐Gupta Efficiency (KGE) scores of 0.58 and 0.76 at large and local stations, respectively. We further assess the impact of reservoirs through different simulation schemes, revealing that reservoirs significantly alter DOC fluxes by regulating streamflow patterns and promoting DOC mineralization. Model simulations indicate that reservoirs reduce total DOC flux from the Mississippi River into the ocean by 7.5%, with the long‐term average annual export decreasing from 3.34 to 3.14 teragrams (Tg) per year. ELM‐MOSART‐DOC integrates process‐based modeling with ML parameterization to enhance the predictive understanding of riverine biogeochemical processes. This approach reduces uncertainties in modeling regional and global carbon cycle ESMs and provides new insights into carbon cycling and its implications for global environmental change.

Li, Lingbo [Univ. of Houston, TX (United States); ↗

Computing with a Chemical Reservoir

Contemporary computation is expensive, with large language models and artificial intelligence becoming more common in daily life. However, high-performance computing is reaching the limits in speed and energy expenditure, and domain science requires ever-increasing computational capacity, with simulations and data analysis pipelines ever-growing in complexity. As we progress towards post-exascale computation, with the associated high energy costs, new methods of energy-conscious computation are required. Novel analog and hybrid digital-analog systems can overcome these challenges, and chemical reactions offer a promising avenue. Computers based on chemistry can provide compact desktop devices with immense computational power. These devices are readily scalable by considering greater reaction systems or vessels, meeting the high-performance requirements for scientific workflows. In this article, we present ChemComp, a compilation pipeline for the conversion of ordinary differential equations into implementable chemical reactions. We then demonstrate the solving capabilities of ChemComp by emulating a potential chemical reservoir device. We leverage the multi-layer intermediate representation (MLIR) compiler framework to implement an expressive chemical reaction abstraction and propose a path for chemical reaction networks (CRNs) to represent mathematical problems effectively. Combined, we demonstrate a potential workflow that can harness chemistry’s computing power to create energy-efficient, high-performance computation systems for contemporary computing needs.

artificial intelligence↗

A Digital Twin Framework for Liquid-cooled Supercomputers as Demonstrated at Exascale

We present ExaDigiT, an open-source framework for developing comprehensive digital twins of liquid-cooled supercomputers. It integrates three main modules: (1) a resource allocator and power simulator, (2) a transient thermo-fluidic cooling model, and (3) an augmented reality model of the supercomputer and central energy plant. The framework enables the study of "what-if" scenarios, system optimizations, and virtual prototyping of future systems. Using Frontier as a case study, we demonstrate the framework's capabilities by replaying six months of system telemetry for systematic verification and validation. Such a comprehensive analysis of a liquid-cooled exascale supercomputer is the first of its kind. ExaDigiT elucidates complex transient cooling system dynamics, runs synthetic or real workloads, and predicts energy losses due to rectification and voltage conversion. Throughout our paper, we present lessons learned to benefit HPC practitioners developing similar digital twins. We envision the digital twin will be a key enabler for sustainable, energy-efficient supercomputing.

Brewer, Wes↗

The Artificial Scientist: in-Transit Machine Learning of Plasma Simulations

Large-scale simulations or scientific experiments produce petabytes of data per run. This poses massive challenges for I/O and storage when scientific analysis workflows are run manually offline. Unsupervised deep learning-based techniques to extract patterns and non-linear relations from these large amounts of data provide a way to build scientific understanding from raw data, reducing the need for manual pre-selection of analysis steps, but require exascale compute and memory to process the full dataset available. In this paper, we demonstrate a heterogeneous streaming workflow in which plasma simulation data is streamed directly to a Machine Learning (ML) application training a model on the simulation data in-transit, completely circumventing the capacity-constrained filesystem bottleneck. This workflow employs openPMD to provide a high level interface to describe scientific data and also uses ADIOS2, to transfer volumes of data that exceed the capabilities of the filesystem. We employ experience replay to avoid catastrophic forgetting in learning from this non-steady state process in a continual manner and adapt it to improve model convergence while learning in-transit. As a proof-of-concept, we approach the ill-posed inverse problem of predicting particle dynamics from radiation in a particle-incell (PIConGPU) simulation of the Kelvin-Helmholtz instability (KHI). We detail hardware-software co-design challenges as we scale PIConGPU to full Frontier, the Top-1 system as of June 2024 Top500 list.

Kelling, Jeffrey [Helmholtz-Zentrum Dresden Rossen↗

Efficiently resolving the terrestrial-aquatic interface in E3SM with sub-grid methods to improve coastal simulations (Final Technical Report)

The broad goal of this project was to extend the capabilities of MPAS‐Ocean, the ocean component of DOE’s Energy Exascale Earth System Model (E3SM), to better resolve the hydrodynamics of the terrestrial‐aquatic interface without significantly increasing computing resource requirements. Specifically, our goal was to better resolve the small-scale features across the terrestrial‐aquatic interface which includes the low lying coastal floodplain and a dendritic network of hydraulically efficient channels connected to estuarine systems and back bays, barrier islands and high energy inlets. The processes driving flow across the terrestrial‐aquatic interface include upland and floodplain hydrology, tides, wind and atmospheric pressure (including coastally generated storm surge across continental shelves and within estuaries and bays), wind waves and water temperature and salinity gradients.

58 GEOSCIENCES↗