Mathematical problems in meteorological modelling / edited by András Bátkai, Petra Csomós, István Faragó, András Horányi, Gabriella Szépszó.

Includes bibliographical references and index.

Foreword; Preface; Contents; Part I Numerical Methods for Meteorological Problems; 1 On a Conservative Finite-Difference Method for 1D Shallow Water Flows Based on Regularized Equations; 1.1 Introduction; 1.2 The 1d Shallow Water System of Equations, Its Regularization and Discretization; 1.3 Numerical Results; References; 2 Discretization in Numerical Weather Prediction: A Modular Approach to Investigate Spectraland Local SISL Methods; 2.1 Introduction; 2.2 Discretization of the Dynamical Core in NWP; 2.2.1 Time Discretization of the Dynamical Core

2.2.2 Space Discretization of the Dynamical Core and Grids2.3 Spectral SISL Discretization Schemes; 2.4 Study of Local SISL Z-Grid Schemes; 2.4.1 The Z-Grid Approach; 2.4.2 Geostrophic Adjustment of Z-Grid Schemes; 2.4.3 SISL Z-Grid Schemes; 2.4.4 Computational Aspects; 2.5 Conclusion and Outlook; References; 3 Turbulence Modeling Using Fractional Derivatives; 3.1 Introduction; 3.2 Preliminaries; 3.3 Results; 3.3.1 The Fractional Newton's Law of Viscosity; 3.3.2 The Algorithm; 3.3.3 The Test Problem; 3.4 Conclusion; Appendix; References

4 A Parallel Numerical Solution Approach for Nonlinear Parabolic Systems Arising in Air Pollution Transport Problems4.1 Introduction; 4.2 The Numerical Solution Process and its Convergence; 4.2.1 Time Discretization; 4.2.2 FEM Discretization in Space; 4.2.3 Outer Iteration: Damped Newton's Method; 4.2.4 Inner Iteration: Preconditioned CG Method Using Equivalent Operator Preconditioning; 4.3 Some Examples in Air Pollution Models; References; Part II Air Quality Modelling; 5 Eulerian and Lagrangian Approaches for Modellingof Air Quality; 5.1 Introduction; 5.2 Eulerian Models

5.3 Lagrangian Models5.3.1 Puff Models; 5.3.2 Trajectory Models; 5.4 Conclusion; References; 6 Hydrodynamic Modeling of Industrial Pollutants Spreading in Atmosphere; 6.1 Introduction; 6.2 General Hydrodynamic Model of Air Circulation; 6.3 A Model of Turbulence; 6.4 A Model of Cloud and Precipitation; 6.5 Numerical Method for Solving the Non-stationary Problem with a Prehistory Based on Interpolation with Multiple Nodes; 6.6 Interpolating Functions, Specified in Macro-Scale Grid Nodes, into the Meso-Scale Grid; 6.7 Approximation of Constituent Members of the Convection-Diffusion

6.8 Solution of the Problem of Impurities Dispersion in the "Near Field"6.9 Conclusion; References; 7 Coordinate Transformation Approach for Numerical Solution of Environmental Problems; 7.1 Introduction; 7.2 A Stationary Model of Air Pollution; 7.3 A Non-stationary Two-Dimensional Problem; 7.4 Positive Splitting Numerical method; 7.5 Conclusions; References; 8 Impact of Climatic Changes on Pollution Levels; 8.1 Introduction; 8.2 Development of Three Climatic Scenarios ; 8.2.1 Climate Scenario 1 (Taking into Account Only the Future Changes of the Temperatures)

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.

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