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

Program Leader:

CONTENTS

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.

1. THE INSTITUTE CWI

Research institute for mathematics and computer science

Scientific departments

• AM: Algebra, Analysis & Geometry (Algebra, discrete mathematics and computer algebra. Modeling and analysis.)
• BS: Operations Research, Statistics & System Theory (Combinatorial optimization and algorithmics. Analysis and control of information flows in networks. System and control theory. Image analysis and spatial stochastics.)
• NW: Numerical Mathematics (Discretization of evolution problems. Boundary-value problems, multigrid and defect correction, Large-scale computing.)
• AP: Software Technology (Computational models. Concurrency and real-time systems. Extensible programming environments. Algebraic and syntactic methods. Logic and language.)
• AA: Algorithms & Architecture (Algorithms and complexity. Cryptography. Interoperable multimedia systems. Databases.)
• IS: Interactive Systems (Computer graphics and visualization. Interaction and parallellism. Interaction and multimedia.)

International cooperation, ERCIM

Funding and personnel

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2. MATHEMATICS & THE ENVIRONMENT

Environmental research

Mathematical modeling

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

Scientific high performance computing and networking (HPCN)

Dynamical systems laboratory

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3. THE PROGRAM'S AIM AND POLICY

Aim of the research program

• The development of advanced mathematics of use for the environmental sciences.
• Strategic and applied multidisciplinary environmental research.
• Transfer of knowledge, interaction and communication with environmental scientists.

Policy criteria for projects

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

• Dr. J.G. Verwer (program leader, committee chairman)
• Dr. W.H. Hundsdorfer (committee secretary)
• Dr. ir. G. van Oortmerssen (general director)
• Prof. dr. ir. O.J. Boxma (department head BS)
• Prof. dr. M. Hazewinkel (department head AM)
• Prof. dr. P.J. van der Houwen (department head NW)

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4. RESEARCH FIELDS

This section briefly describes the research fields and projects within the "Mathematics & the Environment" research program. For more detailed information please contact the projectleaders. More details are also found in CWI's departmental research programs.

Research fields

1. Flow and Transport in Porous Media (AM)
2. System Identification of Compartmental Systems (BS)
3. Spatial Statistics (BS)
4. Algorithms for Atmospheric Flow Problems (NW)
5. Algorithms for Coupled Shallow Water/Transport Models (NW)

Abstracts of projects

1. Flow and Transport in Porous Media (AM)
Many important environmental issues are related to transport processes in the subsurface. For instance, the environmental impact of a landfill is to a large extent determined by the way pollutants from that landfill are being transported through the soil system. The same is true for the environmental consequences of oil spills. Another, typically Dutch, example is the salinization of the soil due to salt water intrusion from the sea. Although intensively studied in the past, such phenomena still pose interesting mathematical and modeling questions. Moreover, detailed numerical studies are necessary to improve the prediction capacity of the related models. This project focuses on the following three topics:

1A. Transport of reactive solutes

In collaboration with P. Knabner from the University of Erlangen, models for transport of reactive solutes through porous media were developed. These models, which allow for slow and fast adsorption reactions, were validated at the Agricultural University of Wageningen where column tests were carried out. Of particular practical importance is transport through heterogeneous media. In collabaration with S. van der Zee (Wageningen) we did two dimensional Monte-Carlo simulations in random, physically and chemically heterogeneous media. We also considered more mathematical issues, such as the stability of self-similar and travelling wave solutions arising in transport problems with special geometries. All the results were published in (submitted to) the applied mathematics and the 'porous media' literature.

The NWO Priority Program on "Nonlinear Systems" is acknowledged for financial support.
Contact: Prof.dr.ir. C.J. van Duijn, +31-20-5924208, email: hansd@cwi.nl

1B. Density Induced Flow

Jointly with groups at the National Institute of Public Health and Environmental Protection (RIVM, Bilthoven) and at Delft University of Technology, Department of Civil Engineering, we study mathematical models for flow and transport of fluids in porous media, with (extreme) density contrast. In this case the fluids are fresh and strongly impregnated salt water or brine. We are especially interested in the influence of high density gradients on the dispersivity and so called volume or compressibility effects. The models are developed to explain experimentally observed phenomena and to gain more insight in the nature of density driven flow in porous media. On the other hand, this subject has a close connection to the environmental impact of subsurface storage of chemical and radio active waste in geological salt formations. The emphasis of the CWI contribution to this work is on the mathematical analysis of the governing systems of nonlinear partial differential equations.

Other research topics, related to density driven flow in porous media, are: - Stability analysis of (unstable) flows in porous media. We study the stability of the diffusive zone between fresh groundwater and a plume of polluted, more dense groundwater, as can be found in aquifers beneath waste disposal sites. This leads to a fourth order eigenvalue problem. This is work in collaboration with the RIVM and the Mathematical Institute of Leiden University. - Analysis of a sharp interface model in heterogeneous porous media. A finite element code has been developed and the basic properties of a sharp interface between two fluids, with different density, are studied in relation to permeability and heterogeneity. This is work in collaboration with UniversitŽ de Paris-Sud, France. - Crystal dissolution in porous media. The first part of this study, dealing with travelling wave solutions, has been published. This is work in collaboration with the University of Erlangen, Germany. In the second part we analyse a related Riemann-problem.

The NWO Priority Program on "Nonlinear Systems" is acknowledged for financial support.
Contact: Prof.dr.ir. C.J. van Duijn, +31-20-5924208, email: hansd@cwi.nl or Ruud Schotting, +31-20-5924231, email: ruuds@cwi.nl.

1C. DNAPL infiltration

In this project the infiltration of Dense Non-Aqueous Liquids (DNAPL's) in heterogeneous soils is studied. DNAPL's form a serious threat to ground water quality. They are organic compounds with a density larger than that of water. Therefore they tend to migrate downwards towards the bottom of aquifer systems. Variations in the permeability of the soil, for example the presence of clay lenses in a sandy aquifer, strongly influences the spreading of DNAPL's. Due to capillary effects a DNAPL can only enter a clay lens at high enough saturations. However, once it has entered a clay lens, it becomes a long term source of contamination. Mathematical models of DNAPL infiltration are used to design experiments and to assess remediation strategies. We study the DNAPL infiltration both analytically and numerically. An analysis of the interface conditions between high permeable regions (sand bodies) and low permeable regions (clay lenses) has been carried out. The resulting interface conditions have been incorporated into a numerical simulator.

In this project there is a close cooperation with H. Bruining (Dietz Laboratory, TU Delft). Current cooperation with R. Helmig (IWS, University of Stuttgart) is aimed at defining test problems for DNAPL infiltration that are both practically relevant, and suited to mathematical study.

The NWO Priority Program on "Nonlinear Systems" is acknowledged for financial support. Contact: Prof.dr.ir. C.J. van Duijn, +31-20-5924208, email: hansd@cwi.nl or dr. J. Molenaar, +31-20-5924211, email: hansmo@cwi.nl.

2. System Identification of Compartmental Systems (BS)

System identification of compartmental systems - A mathematical tool in public health and environmental protection.

The aim of this research project is to develop for problems of public health and environmental protection tools in the form of algorithms and theory for system identification of compartmental systems. Compartmental systems is a particular class of dynamic systems that is often used in biology and ecology. Biological or physical modeling leads to a model of several compartments with more or less homogeneous concentrations of materials. The compartments interact by processes of transportation and diffusion. The dynamic behaviour of the concentrations may often in a first approximation be taken as linear. Thus one obtains a mathematical model in the form of a linear compartmental system. Questions posed by public health and environmental protection may be translated into questions for compartmental systems. How to obtain from possibly scarce data a compartmental system that is both realistic and not too complex? How to use such a system for prediction and control?

Research in this project is directed to all aspects of system identification of compartmental systems. The structural identifiability of special cases of compartmental systems arising at the RIVM (National Institute for Public Health and Environmental Protection) have already been studied. Besides, research has been performed and will be continued on the realization problem of positive linear systems.

The project is carried out in cooperation with Dr.ir. P.H.M. Janssen and Dr. P.S.C. Heuberger of the RIVM.

Contact: prof. dr. ir. J.H. van Schuppen, +31 205924085, email: J.H.van.Schuppen@cwi.nl

3. Spatial Statistics (BS)

Spatial Statistics and Oil Pollution in the North Sea

This is a consultancy project, commissioned by RWS (the North Sea Directorate, Ministry of Transport and Public Works). The aim is to develop a reliable statistical method for estimating the spatial variation and the total amount of oil pollution in the Dutch part of the North Sea. Previous work in this project was reported in CWI report BS-N9501 (July 1995). A planar inhomogeneous Poisson point process, with an intensity function which is parametrized by a finite dimensional parameter, was proposed as a spatial model for the locations of the centres of the oil spots. The parametrization enables one to incorporate available a priori knowledge about oil pollution, such as the location of sources of oil pollution (i.e. shipping areas and off-shore locations) and the intensity of shipping in various regions.

In a follow-up study (to be carried out in 1996) the distribution of the volumes of oil spots will be investigated more closely. In particular, attention will be paid to the location of 'big oil spots' as well as to the life time of an oil spot (which depends e.g. on its size and the wind speed). Bootstrap resampling techniques will be employed, with a view towards setting confidence limits for the total amount of oil pollution in a given period. Finally, the choice of the sampling plan (oil spots are observed by a surveillance aircraft with varying frequencies at different locations) employed by RWS to obtain the real data sets used in this study will be under consideration. The question how to choose the sampling plan in an efficient way is still an interesting open problem at present.

The RWS is acknowledged for financial support.
Contact: dr. R. Helmers, +31 205924079, email: R.Helmers@cwi.nl

4. Algorithms for Atmospheric Flow Problems (NW)

4A. CIRK: Mathematical modeling of global transport and chemistry of trace constituents in the troposphere

The CIRK project is concerned with atmospheric research and mathematical models. The subject of study is the expected change of atmospheric chemical composition due to ever increasing emissions of polluting species. The development and use of mathematical models which can predict atmospheric transport, chemistry and exchange of trace constituents, is essential for this research. Four research groups from four Dutch institutes are involved in CIRK ('CIRK' emanates from putting together the first letter of their names). The institutes are CWI, IMAU (Institute for Marine and Atmospheric Research, University of Utrecht), RIVM (National Institute of Public Health and Environmental Protection, Bilthoven), and KNMI (Royal Netherlands Meteorological Institute, de Bilt). The scientific disciplines represented in the four research groups are atmospheric chemistry, meteorology, computational fluid dynamics and numerical mathematics.

The specific goal is to develop a 3D model for the global troposphere, including troposphere/ stratosphere exchange processes, for predictions over extensive periods of time. As regards the mathematical description, this model consists of a large system of time-dependent partial differential equations of the advection-diffusion-reaction type, supplemented with subgrid scale, physical parameterizations. Besides physical knowledge, efficient algorithms and computer capacity is and will remain a critical factor for resolution. Within the CIRK project, numerical mathematics and HPCN research therefore gets a high priority. This part of the project is carried out at CWI. Among others, attention is given to fast stiff ODE solvers for the atmospheric chemistry problem, advection schemes, schemes for solving turbulent diffusion and stiff chemistry coupled, operator splitting and local refinement or zooming techniques.

The RIVM and Cray Research Inc. are acknowledged for financial support.
Contact: dr. J.G. Verwer, +31 205924095, email: Jan.Verwer@cwi.nl

4B. LOTOS: Atmospheric air pollution.

This project is carried out jointly with the Department of Environmental Chemistry of MEP-TNO (TNO Institute for Environment, Energy and Process Innovation) and is part of the HPCN project 'HPCN for Environmental Applications' which is mentioned at the end of Section 5 where activities of the research consortium TASC are described.

The subject of study are the numerical algorithms of LOTOS, a dispersion model of MEP-TNO for 'LOng Term Ozone Simulation'. This model is currently used for a variety of environmental studies related to air pollution. The aim of the project is to significantly enhance the computational efficiency of LOTOS. Hereby, the development of a three-dimensional, parallel LOTOS is one of the main issues. Therefore the focus lies on numerical algorithms and parallelization. Among others, attention will be given to fast stiff ODE solvers for the atmospheric chemistry problem, advection schemes, schemes for solving turbulent diffusion and stiff chemistry coupled, operator splitting and local refinement or zooming techniques.

The Dutch HPCN program is acknowledged for financial support.
Contact: dr. J.G. Verwer, +31 205924095, email: Jan.Verwer@cwi.nl

5. Algorithms for Coupled Shallow Water/Transport Models (NW)

5A. Three-dimensional coupled shallow-water/transport modeling

The study of pollution and sediment transport in shallow seas requires a three-dimensional dynamic simulation of the hydrodynamics and the sediment/pollutant transport. Such a combined simulation is one of the objectives of the international research program NOWESP (NOrth West European Shelf Program), which is embedded in the EEC project MAST II (MArine Science and Technology). NOWESP concentrates on the continental shelf and studies (i) effects of dispersal of Rhine water and other major West-European rivers in the North Sea, (ii) quantification of biogeochemical fluxes, and (iii) behaviour of the shelf as interaction between land and ocean. Since the simulations include long-term effects, a huge computational task is faced.

Currently, in NOWESP the emphasis is on the analysis of existing data sets of measurements with respect to reliability, variability and trends and on the estimation of fluxes and budgets based on this analysis. CWI is involved in the subtask "Evaluation of the possibilities of hardware/software developments for new generation flux models". CWI research concentrates on solving numerically three-dimensional flux models. Our research contributions deal with parallelization and vectorization of solvers and adaptive-grid methods to accurately resolve local regions of high spatial activity. See also the related task 5B.

Within the Netherlands co-operation exists with RWS, ICIM, Delft Hydraulics, TUD (Parallel Algorithms Group, Faculty of Applied Math. and Comp. Sc.). This co-operation takes place in the framework of the research consortium TASC (see Section 5).

Financial support is obtained from the EC.
Contact: prof. dr. P.J. van der Houwen, +31 205924083, email: P.J.van der Houwen@cwi.nl

5B. HPCN project: Surface water pollution.

This project is carried out jointly with WL (Delft Hydraulics) and TUD (Technical University Delft) and is part of the HPCN project 'HPCN for Environmental Applications' which is mentioned at the end of Section 5 as a TASC activity.

The subject of study are Eulerian grid transport models for solving a variety of surface water pollution problems. The focus lies on numerical algorithms and parallelization. Specific numerical techniques include domain decomposition for the parallelization based on explicit interface conditions. This type of decomposition is made possible by a tailored splitting approach which treats vertical transport implicitly and horizontal transport explicitly. The splitting used is of Hopscotch type. Starting point for the project is the 3D code TRUST (Transport and Reactions Unified by Splitting Techniques) which is currently written at CWI.

The Dutch HPCN program is acknowledged for financial support.
Contact: prof. dr. P.J. van der Houwen, +31 205924083, email: P.J.van der Houwen@cwi.nl

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5. Consortium TASC: Transport Applications and Scientific Computing

For densely populated and industrialized countries, control of levels of pollution is becoming more and more important in view of the growing awareness of damaging effects. Reduction of pollution is in general an expensive procedure leading to high costs for society and industry. It is therefore necessary to determine as accurately as possible critical levels and to reduce and control pollution optimally so as to minimize costs. This is a very difficult task and requires complicated simulation models which have to be run on high-speed computers.

Simulation of long-range transport and exchange of chemical and biochemical constituents is of major importance, as pollution phenomena are almost never limited to areas where dangerous pollutants are emitted. Mathematically, transport simulation models are based on mass balance equations constituted by systems of time-dependent partial differential equations, describing fluid flow, transport, chemical and biochemical processes. This makes transport simulation computationally highly expensive. In fact, computer capacity is one of the major limiting factors for three-dimensional simulations in practice. High performance computing is therefore a prerequisite for developing truly qualified transport simulation software. It will enable improving accuracy of predictions considerably. This can be used to advantage in determining cost-effective ways for controlling and/or reducing levels of hazardous pollution.

Research groups from CWI, IMAU, RIVM, RWS, TNO, TUD and WL have formed the interdisciplinary research consortium TASC (Transport Applications and Scientific Computing). The objective is to develop highly efficient, parallel software for three-dimensional (3D) transport simulation. Three main tasks are distinguished: (I) Numerical algorithm and software development, (II) Implementation of fully integrated models, and (III) Application to real life problems. All partners are already active in the field and involved in various joint projects. CWI and TUD will contribute mainly to task (I). IMAU, RWS, RIVM, WL and TNO are end users and the application-oriented partners and will contribute mainly to tasks (II) and (III).

The TASC partners CWI, TNO, TUD and WL participate in the Dutch HPCN program through the project 'HPCN for Environmental Applications'. This project will start January 1996 and is planned to last 4 years. Research activities concern simulation of atmospheric air pollution (see project 4B) and pollution in shallow water (see project 5B). A detailed project description of this complete HPCN project can be obtained from

Contact: dr. J.G. Verwer, +31 205924095, email: Jan.Verwer@cwi.nl
The Dutch HPCN program is acknowledged for financial support.

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6. SYMPOSIA

To promote national and international collaboration in research in Environmental Mathematics, CWI organizes a series of symposia entitled Topics in Environmental Mathematics. Each symposium will focus on a topic of interest to mathematicians and environmental scientists from a particular field. Up to now the following meetings have taken place:
1. 'Analytical and Numerical Aspects of Modeling Groundwater Pollution'; CWI, Jan. 31, 1992. This meeting was organized jointly with IBM Nederland N.V. and RIVM.
2. 'Numerical Aspects of Atmospheric Transport Models'; CWI, Dec. 18, 1992.
3. 'Modeling Aspects of Atmospheric Transport Models'; CWI, Feb. 26, 1993.
4. 'Statistics for the Environment'; CWI, Dec. 17, 1993.
5. 'Numerical Algorithms for Atmospheric Transport-Chemistry Problems'; CWI, May 18, 1994.
6. 'First Symposium Transport Algorithms and Scientific Computing'; CWI, Feb. 24, 1995. This meeting was organized in the framework of the TASC consortium (see Section 5).
7. 'Second Symposium Transport Algorithms and Scientific Computing'; CWI, June 9, 1995. This meeting was organized in the framework of the TASC consortium (see Section 5).
8. 'Third Symposium Transport Algorithms and Scientific Computing'; CWI, Sept. 8, 1995. This meeting was organized in the framework of the TASC consortium (see Section 5).
9. 'System Identification and Modeling for Environmental Problems'; CWI, Nov. 22, 1995.

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7. CONSULTATION SERVICES

Transfer of knowledge is part of CWI's mission and many CWI researchers are involved in short or long term consultation services. Transfer of knowledge, interaction and communication with the environmental science community is also an important aim of the environmental research program. CWI can offer a broad expertise on virtually any discipline from mathematics and computer science.

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8. ADDRESS LIST

EERO	European Environmental Research Organization
	Generaal Foulkesweg 70
	P.O. Box 191
	6700 AD Wageningen
	The Netherlands
	Tel. 0317-484816/484817

DNMI	Norwegian Meteorological Institute
	P.O. Box 43
	Blindern
	N-0313 Oslo
	Norway

IBM	IBM Nederland N.V.
	Boerhaavelaan 11
	P.O. Box 60
	2700 AB Zoetermeer
	The Netherlands
	Tel. 079 - 3253111

IBM	Bergen Scientific Centre, IBM
	Thormølensgate 55
	N-5008 Bergen
	Norway
	Tel. + 47 - 5 - 544620
	
IB-DLO	Institute for Soil Fertility Research
	P.O. Box 30003
	9750 RA Haren
	The Netherlands
	Tel. 050 - 5337777

IFT	Institut für Troposphärenforschung e.V.
	Permoserstr. 15
	04303 Leipzig
	Germany

IMAU	University of Utrecht
	Institute for Marine and Atmospheric Research
	Princetonplein 5
	P.O. Box 80.005
	3508 TA Utrecht
	The Netherlands

CDI	Central Veterinary Institute
	P.O. Box 65
	8200 AB Lelystad
	The Netherlands
	Tel. 0320 - 273911

KEMA	KEMA Nederland BV
	Utrechtseweg 310
	P.O. Box 9035
	6800 ET The Netherlands

KNMI	Koninklijk Nederlands Meteorologisch Instituut
	Wilhelminalaan 10
	P.O. Box 201
	3730 AE de Bilt
	The Netherlands
	Tel. 030 - 2206911

LUW	Agricultural University Wageningen
	Department of Mathematics, Dreijenlaan 4
	P.O. Box 9101
	6700 HB Wageningen
	The Netherlands
	Tel. 0317 - 484385 / 482386

NERI	National Environmental Research Institute
	Air Pollution Laboratory
	Frederiksborgvej 399
	DK-4000 Roskilde
	Denmark
	Tel. + 45 46 301200

RIVM1	National Institute of Public Health and Environmental Protection,
	Antonie van Leeuwenhoeklaan 9
	Air Laboratory
	P.O. Box 1
	3720 BA Bilthoven
	The Netherlands
	Tel. 030 - 2749111

RIVM2	National Institute of Public Health and Environmental Protection,
	Antonie van Leeuwenhoeklaan 9
	Laboratory for Soil and Groundwater Research
	P.O. Box 1
	3720 BA Bilthoven
	The Netherlands
	Tel. 030 - 2749111

RL	University of Limburg, Tongersestraat 53 
	Faculty of General Science
	Department of Mathematics
	P.O. Box 616
	6200 MD Maastricht
	The Netherlands
	Tel. 043 - 3887496

RWS/RIKZ National Institute for Coastal and Marine Management/RIKZ
	Kortenaerkade 1
	P.O. Box 20907
	2500 EX The Hague
	The Netherlands
	Tel.  070 - 3114311 

TNO	TNO Institute of Applied Geoscience
	Schoemakerstraat 97
	P.O. Box 6012
	2600 JA Delft
	Tel. 015 - 2697113

TNO-MEP	TNO Institute for Environment, Energy and Process Innovation
	Department of Environmental Chemistry 
	Schoemakerstraat 97
	P.O. Box 6011
	2600 JA Delft
	Tel. 015 - 2697113

TUD	Technische Universiteit Delft
	Mekelweg 4
	Vakgroep Toegepaste Analyse
	Postbus 5031
	The Netherlands
	2600 GA Delft
	 
VUA	Vrije Universiteit
	De Boelelaan 1081
	Wiskundig Seminarium
	Postbus 7161
	1007 MC Amsterdam
	The Netherlands
	Tel. 020 - 4447700

WL	Delft Hydraulics
	Rotterdamseweg 185
	Postbus 177
	2600 MH Delft
	The Netherlands
	Tel. 015 - 2569353

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Go to the CWI project overview or to the CWI home page.

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Joke Blom (gollum@cwi.nl)
Last update 96/06/25.