Research Program Mathematics & the Environment
(terminated 1997, cf. Environmental Modelling and Porous Media Research (MAS1))

Program Leader:

Dr. J.G. Verwer
To a large extent, environmental research is multidisciplinary and involves sciences like atmospheric chemistry, meteorology, oceanography, hydrology, biology, physics, fluid dynamics, mathematics and computer science. Mathematics and computer science occupy a special place here because many of the environmental problems being studied do not permit experimentation. Mathematical models and computer simulation are being used more and more as the appropriate means to gain insight and their use in solving research problems in many different application fields is well acknowledged. CWI has a broad expertise in the mathematical and computer sciences and carries out a number of mathematical research projects connected with environmental problems. These projects constitute CWI's "Mathematics & the Environment" research program. This document describes the field, the purpose of this program, and the research projects for 1996 and the near future.


  1. The institute CWI.
  2. Mathematics & the Environment.
  3. The program's aim and policy.
  4. Research fields.
  5. Consortium TASC.
  6. Symposia.
  7. Consultation services.
  8. Address list.


Research institute for mathematics and computer science

CWI is the Dutch national research institute for mathematics and computer science. CWI's goal is the promotion of advanced research into mathematics and computer science, with special emphasis on areas to which the research has relevant applications. For CWI, environmental research provides an important subject area for applied research into mathematics and computer science. CWI is supported by the government through "The Netherlands Organization for Scientific Research" (NWO). Other important resources come from a variety of national and international research programs and contract research for industry and public authorities.

Scientific departments

CWI has six scientific departments, of which three focus on mathematics and three on computer science. Below, in parentheses, the current research fields of these departments are listed:

International cooperation, ERCIM

One of CWI's goals is to promote international cooperation and to support international projects. Many individual contacts are held by the researchers. In addition, CWI takes part in ERCIM (European Research Consortium for Informatics and Mathematics). Other national institutes from Europe include AEDIMA (Spain), CNR (Italy), FORTH (Greece), GMD (Germany), INRIA (France), INESC (Portugal), DRAL (England), SICS (Sweden), SGFI (Switzerland), SINTEF (Norway), SZTAKLI (Hungary) and VTT (Finland). An important ERCIM goal is to foster collaborative work within the European research community and to increase co-operation with European industries. ERCIM organizes workshops and courses, promotes training and undertakes joint strategic projects.

Funding and personnel

NWO is the main source of funding and currently provides about 70% of CWI's budget. The remaining 30% is obtained from other sources, for instance special European programmes (ESPRIT), national programmes (STW, IOP), contract research for industry and government organizations, and services delivered by supporting sectors. Early 1996 the total number of own personnel amounts to 143 fte (full time equivalents), divided over the mathematics departments (40 fte), the computer science departments (49 fte), and the supporting sectors (management, library, computer support, etc. 54 fte). CWI also hosts a great number of researchers in externally financed positions, early 1996 about 57 fte.


Environmental research

The term "environmental research" covers a wide range of scientific activities in many natural sciences. Environmental research is multidisciplinary and involves sciences like atmospheric physics and chemistry, meteorology, oceanography, hydrology, geology, biology, physics, fluid dynamics and mathematics together with the computer sciences. Mathematics is vital since it is an essential resource for setting up theories and models for a wide diversity of problems. Mathematics provides a universal language for modeling purposes in the natural sciences and disciplines from industry and engineering.

Mathematical modeling

Especially in industry and engineering this has been acknowledged for a long time now, resulting in a high state-of-the-art of mathematical modeling. Since World War II one observes the systematic replacement of much experimentation in design and problem solving by mathematical modeling, as this is mostly cheaper, more versatile and faster. The advent of very fast super and parallel computers with large memories has accelerated this process. For instance, every modern aircraft is a product of computer aided design leaning for a significant part upon achievements from mathematics, computational fluid dynamics and computer science.

In recent years there is a growing recognition that resources for environmental research should be increased significantly in order to advance our understanding of the working of the environment and all aspects of pollution. Also the Dutch government expresses its concern with the environment regularly and has allocated several funds for a variety of activities in the environmental sector. These activities should include both long-term strategic and applied research, implying that research in sciences basic to the study of environmental problems must continue to be supported.

The mathematical and computer sciences belong to this category, since by the complexity of most of the environmental pollution problems they can only be investigated with the use of computer models based on mathematical techniques. Our ability to understand and interprete models for environmental problems relies in large part on mathematics and computer simulation. Applications of models exist from diverse fields such as biosphere dynamics, population dynamics, hydrology, porous media, atmospheric physics, global energy and climatic change. Also studies concerned with the behaviour and fate of highly toxic, chemical compounds in the environment necessitate an extensive use of simulation models.

Mathematical research fields

Research activities covered by this program may concern theory, experimentation, algorithms, computer implementation, and may interface with virtually any mathematical and computational discipline. We mention, for instance, analysis of differential equations and numerical mathematics, scientific computing and computational fluid dynamics, large-scale modeling on super and parallel computers, visualization and massive-data handling, population dynamics, biomathematics, dynamical system theory and chaos, statistics, operations research, optimization and optimal control, image reconstruction, inverse methods and parameter estimation, etc.

Scientific high performance computing and networking (HPCN)

A development which cannot be ignored is the rapidly increasing significance of scientific high performance computing and networking. From the Rubbia report we quote, "The field of computing is on the verge of a new revolution. During recent years the amount of computational power at the disposal of scientists and engineers (super and parallel computers) has increased dramatically. This has enabled them to envisage approaches that will revolutionize all fields of science". Another quotation from this report reads "Scientific and societal progress, industrial competiveness, the understanding and control of environmental factors necessary to human well- being will be governed by the availability of adequate computing power".

Dynamical systems laboratory

The AM department has installed a dynamical systems laboratory, the purpose of which is to make available a collection of user-friendly software and hardware for the computer assisted analysis of dynamical systems. Such a laboratory, provided with a.o. an interactive interface and facilities for graphical output, has much to offer for the study of mathematical models arising in environmental research. In particular, it can assist environmental scientists who are faced with the growing complexity of environmental and mathematical modelling, in the sense that with the tools of a dynamical systems lab they are better able to concentrate on their problem formulation and validation and less hindered by purely mathematical difficulties. At present, most tools are suitable for dynamical systems on low dimensional spaces only, but in the future attention will be devoted to high (even infinite) dimensional situations as well. The lab has close connections with the NWO priority program Nonlinear Systems.


Aim of the research program

Science and technology have benefitted greatly from the systematic use of mathematics. As a result, there exists nowadays a unanimous opinion that mathematics is increasingly vital to science and technology, and therefore to society itself. In line with this development, the aim of CWI's research program "Mathematics & the Environment" is to contribute to

Policy criteria for projects

The policy for entering existing and new CWI projects in this program is based on three main criteria:
  1. To safeguard the aim of developing and promoting advanced mathematical techniques in environmental research, projects should directly aim at real applications. Various ways of combining mathematics with applications are conceivable (joint work with environmental scientists, publications in environmental literature, contract research).
  2. To capitalize on past successful CWI research, as well as to maintain a high scientific quality, projects should relate sufficiently well with existing research programs of the scientific departments. A sufficient degree of in-house expertise should be available, either from existing CWI staff, or from long-term visiting researchers.
  3. To promote transfer of knowledge, attention should be given to projects that also serve an educational purpose and involve Ph-D or post-doc research. This is important because there is a growing need for young, skilled scientists in multidisciplinary environmental research.

Program committee

The program will be discussed at regular times by the program committee. The task of the committee is to discuss the scientific relevance of the research carried out in the various projects, to discuss the program in connection with CWI's general research policy, etc. The current composition is: