Author: Bertrand Chapron Publisher: Springer Nature ISBN: 3031400941 Category : Mathematics Languages : en Pages : 347
Book Description
This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.
Author: Robert Adler Publisher: Springer Science & Business Media ISBN: 1461224306 Category : Mathematics Languages : en Pages : 473
Book Description
The study of the ocean is almost as old as the history of mankind itself. When the first seafarers set out in their primitive ships they had to understand, as best they could, tides and currents, eddies and vortices, for lack of understanding often led to loss of live. These primitive oceanographers were, of course, primarily statisticians. They collected what empirical data they could, and passed it down, ini tially by word of mouth, to their descendants. Data collection continued throughout the millenia, and although data bases became larger, more re liable, and better codified, it was not really until surprisingly recently that mankind began to try to understand the physics behind these data, and, shortly afterwards, to attempt to model it. The basic modelling tool of physical oceanography is, today, the partial differential equation. Somehow, we all 'know" that if only we could find the right set of equations, with the right initial and boundary conditions, then we could solve the mysteries of ocean dynamics once and for all.
Author: Bertrand Chapron Publisher: Springer Nature ISBN: 3031189884 Category : Mathematics Languages : en Pages : 324
Book Description
This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.
Author: John Norbury Publisher: Cambridge University Press ISBN: 9780521806817 Category : Mathematics Languages : en Pages : 402
Book Description
The complex flows in the atmosphere and oceans are believed to be accurately modelled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems. The simplifications often result in models that are amenable to solution both analytically and numerically. This volume and its companion explain why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations. They show how geometry and analysis facilitate solution strategies.
Author: Kyprianos Agioub Gkirgkis Publisher: ISBN: Category : Languages : en Pages : 255
Book Description
The present work focuses on applying the Dynamically Orthogonal Primitive Equations (DO-PE) for realistic high-resolution stochastic ocean forecasting in regions with complex ocean dynamics. In the first part, we identify and test a streamlined process to create multi-region initial conditions for the DO-PE framework, starting from temporally and spatially sparse historical data. The process presented allows us to start from a relatively small but relevant set of measured temperature and salinity historical vertical profiles (on the order of hundreds) and to generate a massive set of initial conditions (on the order of millions) in a stochastic subspace, while still ensuring that the initial statistics respect the physical processes, modeled complex dynamics, and uncertain initial conditions of the examined domain. To illustrate the methodology, two practical examples-one in the Gulf of Mexico and another in the Alboran Sea--are provided, along with a review of the ocean dynamics for each region. In the second part, we present a case study of three massive stochastic DO-PE forecasts, corresponding to ensembles of one million members, in the Gulf of Mexico region. We examine the effect of adding more dynamic DO modes (i.e., stochastic dimensions) and show that it tends to statistical convergence along with an enhancement of the uncertainty captured by the DO forecast realizations, both by increasing the variance of already existing features as well as by adding new uncertain features. We also use this case study to validate the DO-PE methodology for realistic high-resolution probabilistic ocean forecasting. We show good accuracy against equivalent deterministic simulations, starting from the same initial conditions and simulated with the same assumptions, setup, and original ocean model equations. Importantly, by comparing the reduced-order realizations against their deterministic counterparts, we show that the errors due to the DO subspace truncation are much smaller and growing slower than the fields themselves are evolving in time, both in the Root Mean Square Error (RMSE) sense as well as in the 3D multivariate ocean field sense. Based on these observations, we conclude that the DO-PE realizations closely match their full-order equivalents, thus enabling massive forecast ensembles with practically low numerical errors at a tractable computational cost.
Author: John Marshall Publisher: Academic Press ISBN: 0080954561 Category : Science Languages : en Pages : 345
Book Description
For advanced undergraduate and beginning graduate students in atmospheric, oceanic, and climate science, Atmosphere, Ocean and Climate Dynamics is an introductory textbook on the circulations of the atmosphere and ocean and their interaction, with an emphasis on global scales. It will give students a good grasp of what the atmosphere and oceans look like on the large-scale and why they look that way. The role of the oceans in climate and paleoclimate is also discussed. The combination of observations, theory and accompanying illustrative laboratory experiments sets this text apart by making it accessible to students with no prior training in meteorology or oceanography. * Written at a mathematical level that is appealing for undergraduates and beginning graduate students * Provides a useful educational tool through a combination of observations and laboratory demonstrations which can be viewed over the web * Contains instructions on how to reproduce the simple but informative laboratory experiments * Includes copious problems (with sample answers) to help students learn the material.