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This book gives a research exposition of interdisciplinary topics at the cutting edge of the applied mathematics of climate change and long range weather forecasting through a hierarchy of models with contemporary applications to grand challenges such as intraseasonal weather prediction. The developments include recent physics constrained low-order models, new analog prediction models, and equation free methods to capture intermittency and low frequency variabilities in massive datasets through Nonlinear Laplacian Spectral Analysis (NLSA) which combines delayed embeddings, causal constraints, and machine learning. Applications to grand challenges such as tropical intraseasonal variability of the Madden-Julian Oscillation (MJO) and the Monsoon as well as sea ice re-emergence in the Arctic on yearly time scales. A highlight is the exposition and pedagogical development of recent intermediate stochastic skeleton models to capture the main features of the MJO through PDE ideas, stochastics, and physical reasoning and compared with observational data. The mathematical theory of model error and the use of information theory combined with linear statistical response theory in a calibration stage are applied to improve long range forecasting and multi-scale data assimilation with concrete examples.
Zusammenfassung: This highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book's individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptions of time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the world around us. This edited collection presents new ways of forecasting, introduces new means of control, and - perhaps as the most demanding task - it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the development fields discussed, to demonstrate their mathematical complexity and, more importantly, to encourage mathematicians to contribute to the further success of such practical applications as weather forecasting and climate change projections. Written by leading experts in the field, the book provides an attractive and diverse introduction to areas in which mathematicians and modellers from the meteorological community can cooperate and help each other solve the problems that operational weather centres face, now and in the near future. Readers engaged in meteorological research will become more familiar with the corresponding mathematical background, while mathematicians working in numerical analysis, partial differential equations, or stochastic analysis will be introduced to further application fields of their research area, and will find stimulation and motivation for their future research work.
Forecasting the weather for the long and medium range is a difficult and scientifically challenging problem. Since the first operational weather prediction by numerical methods was carried out (on the BESK computer in Stockholm, Sweden, 1954) . there has been an ever accelerating development in computer technology. Hand in hand has followed a tremendous increase in the complexity of the atmospheric models used for weather prediction. The ability of these models to predict future states of the atmosphere has also increased rapidly, both due to model development and due to more accurate and plentiful observations of the atmosphere to define the initial . state for model integrations. It may however be argued on theoretical grounds that even if we have an almost perfect model with almost perfect initial data, we will never be able to make an accurate weather prediction more than a few weeks ahead. This is due to the inherent instability of the atmosphere and work in this field was pioneered by E. Lorenz. It is generally referred to as atmospheric predict ability and in the opening chapter of this book Professor Lorenz gives us an overview of the problem of atmospheric predictability. The contributions to this book were originally presented at the 1981 ECMWF Seminar (ECMWF - European Centre for Medium Range Weather Forecasts) which was held at ECMWF in Reading, England, in September 1981.
Mathematical models are very much in the news now, as they are used to make decisions about our response to such vital areas as COVID-19 and climate change. Frequently, they are blamed for a series of dubious decisions, creating much concern amongst the general public. However, without mathematical models, we would have none of the modern technology that we take for granted, nor would we have modern health care, be able to forecast the climate, cook a potato, have electricity to power our home, or go into space.By explaining technical mathematical concepts in a way that everyone can understand and appreciate, Climate, Chaos and COVID: How Mathematical Models Describe the Universe sets the record straight and lifts the lid off the mystery of mathematical models. It shows why they work, how good they can be, the advantages and disadvantages of using them and how they make the modern world possible. The readers will be able to see the impact that the use of these models has on their lives, and will be able to appreciate both their power and their limitations.The book includes a very large number of both short and long case studies, many of which are taken directly from the author's own experiences of working as a mathematical modeller in academia, in industry, and between the two. These include COVID-19 and climate and how maths saves the whales, powers our home, gives us the material we need to live, and takes us into space.
As the nation's economic activities, security concerns, and stewardship of natural resources become increasingly complex and globally interrelated, they become ever more sensitive to adverse impacts from weather, climate, and other natural phenomena. For several decades, forecasts with lead times of a few days for weather and other environmental phenomena have yielded valuable information to improve decision-making across all sectors of society. Developing the capability to forecast environmental conditions and disruptive events several weeks and months in advance could dramatically increase the value and benefit of environmental predictions, saving lives, protecting property, increasing economic vitality, protecting the environment, and informing policy choices. Over the past decade, the ability to forecast weather and climate conditions on subseasonal to seasonal (S2S) timescales, i.e., two to fifty-two weeks in advance, has improved substantially. Although significant progress has been made, much work remains to make S2S predictions skillful enough, as well as optimally tailored and communicated, to enable widespread use. Next Generation Earth System Predictions presents a ten-year U.S. research agenda that increases the nation's S2S research and modeling capability, advances S2S forecasting, and aids in decision making at medium and extended lead times.
Numerical weather prediction models play an increasingly important role in meteorology, both in short- and medium-range forecasting and global climate change studies. The most important components of any numerical weather prediction model are the subgrid-scale parameterization schemes, and the analysis and understanding of these schemes is a key aspect of numerical weather prediction. This book provides in-depth explorations of the most commonly used types of parameterization schemes that influence both short-range weather forecasts and global climate models. Several parameterizations are summarised and compared, followed by a discussion of their limitations. Review questions at the end of each chapter enable readers to monitor their understanding of the topics covered, and solutions are available to instructors at www.cambridge.org/9780521865401. This will be an essential reference for academic researchers, meteorologists, weather forecasters, and graduate students interested in numerical weather prediction and its use in weather forecasting.
The Gap Between Weather and Climate Forecasting: Sub-seasonal to Seasonal Prediction is an ideal reference for researchers and practitioners across the range of disciplines involved in the science, modeling, forecasting and application of this new frontier in sub-seasonal to seasonal (S2S) prediction. It provides an accessible, yet rigorous, introduction to the scientific principles and sources of predictability through the unique challenges of numerical simulation and forecasting with state-of-science modeling codes and supercomputers. Additional coverage includes the prospects for developing applications to trigger early action decisions to lessen weather catastrophes, minimize costly damage, and optimize operator decisions. The book consists of a set of contributed chapters solicited from experts and leaders in the fields of S2S predictability science, numerical modeling, operational forecasting, and developing application sectors. The introduction and conclusion, written by the co-editors, provides historical perspective, unique synthesis and prospects, and emerging opportunities in this exciting, complex and interdisciplinary field.
This book recommends research priorities and scientific approaches for global change research. It addresses the scientific approaches for documenting global change, developing integrated earth system models, and conducting focused studies to improve understanding of global change on topics such as earth system history and human sources of global change.