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Abstract: "Due to the large number of chemical species and the three space dimensions, off-the-shelf stiff ODE integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations [formula] from the field of air pollution modelling. This has led to the use of special time integration techniques. This paper is devoted to a survey of such techniques, encompassing stiff chemistry solvers, positive advection schemes, time or operator splitting, implicit-explicit methods and approximate matrix factorization solutions. Of great importance in practice is high performance computing due to the huge problem scales, in particular for global models. We will therefore also report on experiences with vector/parallel shared memory and massively parallel distributed memory architectures and clusters of workstations. The survey is not entirely unique to air pollution models and biased towards work done at CWI over approximately the last 5 years."
"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 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.
This book collates the written contributions of the Second Conference on Air Pollution Modelling and Simulation (APMS 2001). A wide range of current topics is covered, focusing on three challenging issues: (1) the modelling issue of complex, multiphase, atmospheric chemistry; (2) the numerical issue associated with comprehensive three-dimensional chemistry-transport models; and (3) the key issues of data assimilation and inverse modelling. State-of-the art research is presented with many operational procedures applied at either forecast agencies or companies.
This volume contains refereed papers submitted by international experts who participated in the Atmospheric Modeling workshop March 15 -19, 2000 at the Institute for Mathematics and Its Applications (IMA) at the University of Minnesota. The papers cover a wide range of topics presented in the workshop. In particular, mathematical topics include a performance comparison of operator-splitting and non- splitting methods, time-stepping methods to preserve positivity and consideration of multiple timescale issues in the modeling of atmospheric chemistry, a fully 3D adaptive-grid method, impact of rid resolution on model predictions, testing the robustness of different flow fields, modeling and numerical methods in four-dimensional variational data assimilation, and parallel computing. Modeling topics include the development of an efficient self-contained global circulation-chemistry-transport model and its applications, the development of a modal aerosol model, and the modeling of the emissions and chemistry of monoterpenes that lead to the formation of secondary organic aerosols. The volume provides an excellent cross section of current research activities in atmospheric modeling.
Many large mathematical models, not only models arising and used in environmental studies, are described by systems of partial differential equations. The discretization of the spatial derivatives in such models leads to the solution of very large systems of ordinary differential equations. These systems contain many millions of equations and have to be handled over large time intervals by applying many time-steps (up to several hundred thousand time-steps). Furthermore, many scenarios are as a rule to be run. This explains the fact that the computational tasks in this situation are enormous. Therefore, it is necessary to select fast numerical methods; to develop parallel codes and, what is most important when the problems solved are very large to organize the computational process in a proper way.The last item (which is very often underestimated but, let us re-iterate, which is very important) is the major topic of this book. In fact, the proper organization of the computational process can be viewed as a preparation of templates which can be used with different numerical methods and different parallel devices. The development of such templates is described in the book. It is also demonstrated that many comprehensive environmental studies can successfully be carried out when the computations are correctly organized. Thus, this book will help the reader to understand better that, while (a) it is very important to select fast numerical methods as well as (b) it is very important to develop parallel codes, this will not be sufficient when the problems solved are really very large. In the latter case, it is also crucial to exploit better the computer architecture by organizing properly the computational process. - Use of templates in connection with the treatment of very large models - Performance of comprehensive environmental studies - Obtaining reliable and robust information about pollution levels - Studying the impact of future climatic changes on high pollution levels - Investigating trends related to critical levels of pollution
Proceedings of the Millennium NATO/CCMS International Technical Meeting on Air Pollution Modeling and its Application, held May 15-19 in Boulder, Colorado. This volume is the latest in a series of proceedings dating back to 1971. The book addresses the problem of air pollution and reports the latest findings and developments in air pollution modeling, from a truly international list of contributors.
Despite more than 20 years of regulatory efforts, concern is widespread that ozone pollution in the lower atmosphere, or troposphere, threatens the health of humans, animals, and vegetation. This book discusses how scientific information can be used to develop more effective regulations to control ozone. Rethinking the Ozone Problem in Urban and Regional Air Pollution discusses: The latest data and analysis on how tropospheric ozone is formed. How well our measurement techniques are functioning. Deficiencies in efforts to date to control the problem. Approaches to reducing ozone precursor emissions that hold the most promise. What additional research is needed. With a wealth of technical information, the book discusses atmospheric chemistry, the role of oxides of nitrogen (NOx) and volatile organic compounds (VOCs) in ozone formation, monitoring and modeling the formation and transport processes, and the potential contribution of alternative fuels to solving the tropospheric ozone problem. The committee discusses criteria for designing more effective ozone control efforts. Because of its direct bearing on decisions to be made under the Clean Air Act, this book should be of great interest to environmental advocates, industry, and the regulatory community as well as scientists, faculty, and students.
This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.