Editors: István Faragó, Ágnes Havasi, Zahari Zlatev

Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

eBook: US $79 Special Offer (PDF + Printed Copy): US $186
Printed Copy: US $147
Library License: US $316
ISBN: 978-1-60805-777-1 (Print)
ISBN: 978-1-60805-778-8 (Online)
Year of Publication: 2013
DOI: 10.2174/97816080577881130101


High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible.

Mathematical models can be used to predict answers to many important questions about the environment. However, their application will be successful only when several theoretical and practical obstacles are efficiently removed. A successfully applicable mathematical model needs to enable researchers to

  • - Mathematically describe all important physical and chemical processes.
  • - Apply fast and sufficiently accurate numerical methods.
  • - Ensure that the model runs efficiently on modern high speed computers.
  • - Use high quality input data, both meteorological data and emission inventories, in the runs.
  • - Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model.
  • - Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters.
  • - Visualize and animate the output results in order to make them easily understandable even to non-specialists.

This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.


Foreword by László Bozó

Environmental pollution, climate change, the increasing number and intensity of various extreme meteorological and hydrological events have their significant effects on socio-economic activities and the natural systems. Such a tendency could be detected during the past decades, especially for air pollution episodes with high concentrations and depositions, droughts, floods, heavy rainfalls and heat waves.

Sustainable development is one of the key issues of the next decades, including a broad horizon of human activities: e.g. energy production, transport, industrial activity, agriculture, water management, human and animal health care.

Complex environmental modeling, involving experts from the fields of mathematics, physics, chemistry and environmental sciences is needed to analyse, and, as far as possible to predict the sophisticated processes behind this issue. Once the area of environmental problems is targetted, appropriate advanced numerical methods and models are to be developed and tested in order to handle the physical, chemical, biological and even economical processes governing the complex environmental changes.

A number of highly acknowledged scientists contributed to the content of this eeBook. It covers the treatment of some classes of PDEs and ODEs, the implementation of splitting procedures, parallel and grid computations, as well as handling of some classes of inverse problems. One of the most exciting and challenging environmental problems is discussed in Chapter 5: how the climate change influences the level of environmental pollution. The scope of the model classes presented in this eBook is rather broad: it goes from large-scale air pollution model estimations down to street-scale air quality simulations. Regional climate model PRECIS presented here is applying boundary conditions computed by global scale GCMs.

It is now obvious that disciplines of the Earth Sciences can not be treated separately: this eBook shows an example how the representatives of different branches of natural sciences are able to cooperate in addressing and simulating complex environmental issues, expanding our knowledge and providing theoretical and practical support to the readers interested in this field.

László Bozó
Vice President
Hungarian Academy of Sciences’s Section of Earth Sciences

Foreword by Clemens Mensink

Clean air is one of the Earth's natural resources vital to the survival and development of the human population. However, it is often threatened by the impacts of industrial activities, agricultural production, increasing human mobility using fossil fuels, as well as some natural phenomena (e.g. volcanic eruptions). The prospects of a growing world population, a changing climate and further urbanization will even put more pressure on clean air as a critical resource in the future.

Although sources of air pollution may be local, many of the physical and chemical processes influencing air quality take place at a much larger scale. Acidification, ozone formation, transport of particulate matter and radiation effects of nuclear disasters (e.g. Fukushima) may take place over distances of hundreds or even thousands of kilometres and a time scale of several days.

Computer models are needed to understand these processes and provide insights and predictions that may help to evaluate the actual air quality situation or build policies that scientifically underpin sustainable solutions to improve the air quality. The current state-of-the-art large scale air quality models are complex in the sense that need to mathematically couple various processes, such as transport, chemistry, turbulent diffusion, aerosol formation, deposition, etc. All these processes have their own limitations with respect to the time scales they physically consider. This makes an accurate representation of the interactions between these processes a very demanding task, both in terms of scientific understanding as well as with respect to the computer resources needed to resolve the underlying mathematical equations.

The task becomes even more demanding nowadays, since the need for more detailed information is constantly increasing, putting a pressure on the modellers to go to higher resolutions. Representing air pollution concentrations on a domain of 1 km grid resolution covering several regions or countries is more and more becoming the standard. Linking large scale air quality processes to the evaluation and prediction of air quality in cities and streets where people actually live is even a further challenge.

It is clear that a better understanding of the mathematical principles and numerical methods to make these complex models more efficient in using computational resources is a necessary but challenging task. I wish to congratulate the editors of this eBook, Zahari Zlatev, István Faragó and Ágnes Havasi, in providing these insights by collecting the relevant expert contributions of renown specialists in the field. Their contributions are based on sound expertise and experience and form a well balanced mix of theoretical insights and practical applications that go beyond state-of-the-art in environmental modeling in general and air quality modeling in particular.

Clemens Mensink
Unit Manager
Environmental Modeling
VITO, Belgium