Darryl Holm – författare

Mathematics of Planet Earth (MPE) was started and continues to be consolidated as a collaboration of mathematical science organisations around the world. These organisations work together to tackle global environmental, social and economic problems using mathematics.This textbook introduces the fundamental topics of MPE to advanced undergraduate and graduate students in mathematics, physics and engineering while explaining their modern usages and operational connections. In particular, it discusses the links between partial differential equations, data assimilation, dynamical systems, mathematical modelling and numerical simulations and applies them to insightful examples.The text also complements advanced courses in geophysical fluid dynamics (GFD) for meteorology, atmospheric science and oceanography. It links the fundamental scientific topics of GFD with their potential usage in applications of climate change and weather variability. The immediacy of examples provides an excellent introduction for experienced researchers interested in learning the scope and primary concepts of MPE.

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 andoceanography.

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 andoceanography.

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.

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.

This book is based on an Oberwolfach Seminar, and it intends to give an introduction and an overview to several directions of the recent research on stochastic geophysical fluid dynamics and to discuss different geophysical stochastic partial differential equations.

This book is based on an Oberwolfach Seminar, and it intends to give an introduction and an overview to several directions of the recent research on stochastic geophysical fluid dynamics and to discuss different geophysical stochastic partial differential equations.

Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled “Geometric mechanics – variational and stochastic methods” run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Fédérale de Lausanne. The aim of the semester was to develop a common language needed to handle the wide variety of problems and phenomena occurring in stochastic geometric mechanics. It gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to algebra, geometry, topology, representation theory, and dynamical systems theory) and also areas of mathematical physics, control theory, robotics, and the life sciences, with the aim of developing the new research area in a concentrated joint effort, both from the theoretical and applied points of view. The lectures were given by leading specialists indifferent areas of mathematics and its applications, building bridges among the various communities involved and working jointly on developing the envisaged new interdisciplinary subject of stochastic geometric mechanics.

Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled “Geometric mechanics – variational and stochastic methods” run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Fédérale de Lausanne. The aim of the semester was to develop a common language needed to handle the wide variety of problems and phenomena occurring in stochastic geometric mechanics. It gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to algebra, geometry, topology, representation theory, and dynamical systems theory) and also areas of mathematical physics, control theory, robotics, and the life sciences, with the aim of developing the new research area in a concentrated joint effort, both from the theoretical and applied points of view.

The lectures were given by leading specialists indifferent areas of mathematics and its applications, building bridges among the various communities involved and working jointly on developing the envisaged new interdisciplinary subject of stochastic geometric mechanics.