Mathematical Problems In Meteorological Modelling

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.

The material provides an historical background to forecasting developments as well as introducing recent advances. The book will be of interest to both mathematicians and physicians, the topics covered include equations of dynamical meteorology, first integrals, non-linear stability, well-posedness of boundary problems, non-smooth solutions, parameters and free oscillations, meteorological data processing, methods of approximation and interpolation and numerical methods for forecast modelling.

This book contains tutorial and review articles as well as specific research letters that cover a wide range of topics: (1) dynamics of atmospheric variability from both basic theory and data analysis, (2) physical and mathematical problems in climate modeling and numerical weather prediction, (3) theories of atmospheric radiative transfer and their applications in satellite remote sensing, and (4) mathematical and statistical methods. The book can be used by undergraduates or graduate students majoring in atmospheric sciences, as an introduction to various research areas; and by researchers and educators, as a general review or quick reference in their fields of interest.

Numerical Methods in Weather Prediction focuses on the numerical methods for solving problems of weather prediction and explains the aspect of the general circulation of the atmosphere. This book explores the development in the science of meteorology, which provides investigators with improved means of studying physical processes by mathematical stimulation. Organized into eight chapters, this book starts with an overview of the significant physical factors that are instrumental in enriching the theoretical models of weather prediction. This text then examines the system of hydrodynamic equations and the equation of heat transfer related to large-scale atmospheric processes. Other chapters consider the quasigeostrophic approximation model, which is the basis for concepts of the dynamics of atmospheric motions and instrumental in establishing the basic features and laws of evolution of meteorological variables as applied to large-scale processes. The final chapter deals with the adjustment of the humidity field. This book is a valuable resource for meteorologists.

The present monograph is dedicated to a new branch of the theory of climate, which is titled by the authors, "Mathematical Theory of Climate. " The foundation of this branch is the investigation of climate models by the methods of the qUalitative theory of differential equa tions. In the Russian edition the book was named "Fundamentals of the Mathematical Theory of Climate. " Respecting the recommenda tions of Wayne Yuhasz (we are truly grateful to him for this advice), we named the English edition of the book "Mathematics of Climate Modelling. " This title appears to be more appropriate, since the con structive results of the theory are at present preliminary and have not been fully tested with experiments in climate modelling. This branch of science is yet developing and its practical results will be obtained only in the near future. Nevertheless, we want to keep the terminology which we have used in the introduction to the Russian edition of the book, since the authors hope that this term will be accepted by the scientific community for identification of a given branch of climate theory. On preparing the English edition, new ideas were established con necting some significant new research results obtained by the author. We are deeply grateful to G. Marchuk for continual encourage ment of this scientific enterprise and fruitful discussions, to our young colleagues A. Gorelov, E. Kazantsev, A. Gritsun, and A.

This book provides a comprehensive overview of numerical weather prediction (NWP) focusing on the application of the spectral method in NWP models. The author illustrates the use of the spectral method in theory as well as in its application to building a full prototypical spectral NWP model, from the formulation of continuous model equations through development of their discretized forms to coded statements of the model. The author describes the implementation of a specific model - PEAK (Primitive-Equation Atmospheric Research Model Kernel) - to illustrate the steps needed to construct a global spectral NWP model. The book brings together all the spectral, time, and vertical discretization aspects relevant for such a model. It provides readers with information necessary to construct spectral NWP models; a self-contained, well-documented, coded spectral NWP model; and theoretical and practical exercises, some of which include solutions.

This book has as main aim to be an introductory textbook of applied knowledge in Numerical Weather Prediction (NWP), which is a method of weather forecasting that employs: A set of equations that describe the flow of fluids translated into computer code, combined with parameterizations of other processes, applied on a specific domain and integrated in the basis of initial and domain boundary conditions. Current weather observations serve as input to the numerical computer models through a process called data assimilation to produce atmospheric properties in the future (e.g. temperature, precipitation, and a lot of other meteorological parameters). Various case studies will be also presented and analyzed through this book.

New edition of a classic book which was the first comprehensive description of numerical weather prediction.