"Models are often the only way of interpreting measurements to in vestigate long-range transport, and this is the reason for the emphasis on them in many research programs". B. E. A. Fisher: "A review of the processes and models of long-range transport of air pollutants", Atmospheric Environment, 17(1983), p. 1865. Mathematical models are (potentially, at least) powerful means in the efforts to study transboundary transport of air pollutants, source-receptor relationships and efficient ways of reducing the air pollution to acceptable levels. A mathematical model is a complicated matter, the development of which is based on the use of (i) various mechanisms describing mathematically the physical and chemical properties of the studied phenomena, (ii) different mathematical tools (first and foremost, partial differenti al equations), (iii) various numerical methods, (iv) computers (especially, high-speed computers), (v) statistical approaches, (vi) fast and efficient visualization and animation techniques, (vii) fast methods for manipulation with huge sets of data (input data, intermediate data and output data).

The air pollution, and especially the reduction of the air pollution to some acceptable levels, is an important environmental problem, which will become even more important in the next 10-20 years. This problem can successfully be studied only when high-resolution comprehensive models are developed and used on a routinely basis. However, such models are very time-consuming, also when modern high-speed computers are available. Indeed, if an air pollution model is to be applied on a large space domain by using fine grids, then its discretization will always lead to huge computational problems. Assume, for example, that the space domain is discretized by using a (480×480) grid and that the number of chemical species studied by the model is 35. Then several systems of ordinary differential equations containing 8064000 equations have to be treated at every time-step (the number of time-steps being typically several thousand). If a three-dimensional version of the same air pollution model is to be used, then the above figure must be multiplied by the number of layers. It is extremely difficult to treat such large computational problems; even when the fastest computers that are available at present are used.There is an additional great difficulty which is very often underestimated (or even neglected) when large application packages are moved from sequential computers to modern parallel machines. The high-speed computers have normally a very complicated memory architecture and, therefore, the task of producing an efficient code for the particular high-speed computer that is available is both extremely hard and very laborious.The use of standard parallelization tools in the solution of the problems sketched above is discussed in this paper. Results obtained on different types of parallel computers are given. It is demonstrated that the new efficient parallel algorithms allow us to solve more problems and bigger problems.

The protection of our environment is one of the major problems in the society. More and more important physical and chemical mechanisms are to be added to the air pollution models. Moreover, new reliable and robust control strategies for keeping the pollution caused by harmful compounds under certain safe levels have to be developed and used in a routine way. Well based and correctly analyzed large mathematical models can successfully be used to solve this task. The use of such models leads to the treatment of huge computational tasks. The efficient solution of such problems requires combined research from specialists working in different fields. The aim of the NATO Advanced Research Workshop (NATO ARW) entitled “Advances in Air Pollution Modeling for Environmental Security” was to invite specialists from all areas related to large-scale air pollution modeling and to exchange information and plans for future actions towards improving the reliability and the scope of application of the existing air pollution models and tools. This ARW was planned to be an interdisciplinary event, which provided a forum for discussions between physicists, meteorologists, chemists, computer scientists and specialists in numerical analysis about different ways for improving the performance and the quality of the results of different air pollution models.

1. Contents of these proceedings. These proceedings contain most of the papers which were presented at the NATO ARW (Advanced Research Workshop) on "Large Scale Computations in Air Pollution Modelling". The workshop was held, from June 6 to June to, 1998, in Residence Bistritza, a beautiful site near Sofia, the capital of Bulgaria, and at the foot of the mountain Vitosha. 2. Participants in the NATO ARW. Scientists from 23 countries in Europe, North America and Asia attended the meeting and participated actively in the discussions. The total number of participants was 57. The main topic of the discussions was the role of the large mathematical models in resolving difficult problems connected with the protection of our environment. 3. Major topics discussed at the workshop. The protection of our environment is one of the most important problems facing modern society. The importance of this problem has steadily increased during the last two-three decades, and environment protection will become even more important in the next century. Reliable and robust control strategies for keeping the pollution caused by harmful chemical compounds under certain safe levels have to be developed and used in a routine way. Large mathematical models, in which all important physical and chemical processes are adequately described, can successfully be used to solve this task.

The horizontal advection is one of the most important physical processes in an air pollution model. While it is clear how to describe mathematically this process, the computer treatment of the arising first-order partial differential equation (PDE) causes great difficulties. It is assumed that the spatial derivatives in this equation are discretized either by finite differences or by finite elements. This results in a very large system of ordinary differential equations (ODEs). The numerical treatment of this system of ODEs is based on the application of a set of predictor-corrector (PC) schemes with different absolute stability properties. The PC schemes can be varied during the time-integration. Schemes, which are computationally cheaper, are selected when the stability requirements are not stringent. If the stability requirements are stringent, then schemes that are more time-consuming, but also have better stability properties, are chosen. Some norms of the wind velocity vectors are calculated and used in the check of the stability requirements. Reductions of the time-step size are avoided (or, at least, reduced considerably) when the PC schemes are appropriately varied. This leads to an increase of the efficiency of the computations in the treatment of large-scale air pollution models. The procedure is rather general and can also be used in the computer treatment of other large-scale problems arising in different fields of science and engineering.

The protection of our environment is one of the major problems in the society. More and more important physical and chemical mechanisms are to be added to the air pollution models. Moreover, new reliable and robust control strategies for keeping the pollution caused by harmful compounds under certain safe levels have to be developed and used in a routine way. Well based and correctly analyzed large mathematical models can successfully be used to solve this task. The use of such models leads to the treatment of huge computational tasks. The efficient solution of such problems requires combined research from specialists working in different fields. The aim of the NATO Advanced Research Workshop (NATO ARW) entitled “Advances in Air Pollution Modeling for Environmental Security” was to invite specialists from all areas related to large-scale air pollution modeling and to exchange information and plans for future actions towards improving the reliability and the scope of application of the existing air pollution models and tools. This ARW was planned to be an interdisciplinary event, which provided a forum for discussions between physicists, meteorologists, chemists, computer scientists and specialists in numerical analysis about different ways for improving the performance and the quality of the results of different air pollution models.