Mathematical Problems in Meteorological Modelling

Editors: András Bátkai, Petra Csomós, István Faragó, András Horányi, Gabriella Szépszó



Comprehensive overview on problems being important in meteorological modelling

Gives a mathematical insight in meteorological problems, and provides application fields in meteorology for mathematical results

Contains the precise mathematical background and explanation of methods being used 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.

Table of contents (12 chapters)

Front Matter
Pages i-xv

Numerical Methods for Meteorological Problems
Front Matter
Pages 1-2
On a Conservative Finite-Difference Method for 1D Shallow Water Flows Based on Regularized Equations
Pages 3-18
Discretization in Numerical Weather Prediction: A Modular Approach to Investigate Spectral and Local SISL Methods
Pages 19-46
Turbulence Modeling Using Fractional Derivatives
Pages 47-55
A Parallel Numerical Solution Approach for Nonlinear Parabolic Systems Arising in Air Pollution Transport Problems
Pages 57-70

Air Quality Modelling
Front Matter
Pages 71-72
Eulerian and Lagrangian Approaches for Modelling of Air Quality
Pages 73-85
Hydrodynamic Modeling of Industrial Pollutants Spreading in Atmosphere
Pages 87-116
Coordinate Transformation Approach for Numerical Solution of Environmental Problems
Pages 117-127
Impact of Climatic Changes on Pollution Levels
Pages 129-161

Meteorological Data Assimilation and Probabilistic Forecasting
Front Matter
Pages 163-164
An Invitation to Meteorological Data Assimilation
Pages 165-192
Analysis of the Data Assimilation Methods from the Mathematical Point of View
Pages 193-205
Ensemble Methods in Meteorological Modelling
Pages 207-237
Quantifying Sources of Uncertainty in Temperature and Precipitation Projections over Different Parts of Europe
Pages 239-261

Back Matter
Pages 263-264