Krassimir Georgiev

Modeling the long-range transport of air pollutants

NO ONE DOUBTS THAT HIGH CONCENTRATIONS OF air pollutants can damage (either directly or indirectly) plants, animals, and people. But at what point do these concentrations go from acceptable to dangerous level-nd just as importantly, from dangerous to acceptable? Recent environmental studies show that in order to prevent ecosystem destruction, it is absolutely necessary to reduce the concentration and deposition of certain dangerous air pollutants, at least in Europe and North America, to acceptable levels, and keep them there. These are urgent tasks: some damaging effects may soon be irreversible. O n the other hand, because lowering pollution levels is expensive, we need to reduce them to safe levels but no further. T h e critical concentration of a pollutant is the highest concentration that will not damage biological systems over a long period of time, say 50 years. Deposition is the physical process by which air pollutants are returned to the surface of the Earth. There are two deposition mechanisms: d y deposition takes place continuously, and met depos.itioii occurs only during precipitation periods. Concentration and deposition are two separate processes, with significant but different effects on people and the environment; much of the discussion below deals with both. However, for the sake of brevity in this discussion, we’ll use the term “concentration” to mean both concentration and deposition. T h e two problems outlined-establishing critical concentration levels of pollutants and developing effective control strategies to keep pollutants just under those levels--are very complicated, for a t least three reasons:

Advances in air pollution modeling for environmental security

Preface. Acknowledgements. Mathematical modeling of the regional-scale variability of gaseous species and aerosols in the atmosphere A. Aloyan, V. Arutyunyan. Air pollution modeling in action K. Balla et al. Advances in urban meteorology modelling E. Batchvarova, S.-E. Gryning. Modelling studies on the concentration and deposition of air pollutants in East-Central Europe L. Bozo. Estimation of the exchange of sulphur pollution in Southeast Europe H. Chervenkov. Implementing the trajectory-grid transport algorithm in an air quality model D.P. Chock et al. Estimation of air pollution parameters using artificial neural networks H.K. Cigizoglu et al. Some aspects of interaction between operator splitting procedures and numerical methods P. Csomo. Mathematical aspects of data assimilation for atmospheric chemistry models G. Dimitriu, R. Cuciureanu. Fighting the great challenges in large-scale environmental modelling I. Dimov et al. Challenges in using splitting techniques for large-scale environmental modeling I. Dimov et al. Simulation of liberation and dispersion of radon from a waste disposal M. de Lurdes Dinis, A. Fiuza. Methods of efficient modeling and forecasting regional atmospheric processes A.Yu. Doroshenko, V.A. Prusov. Numerical forecast of air pollution - Advances and problems A. Ebel et al. Alternative techniques for studying / modeling the air pollution level L-D. Galatchi. Application of functions of influence in air pollution problems K. Ganev et al. Long-term calculations with a comprehensive nested hemispheric air pollution transport model C. Geels et al. Dispersion modelling for environmental security: principles and their application in the Russian regulatory guideline on accidental releases E. Genikhovich. Higher order non-conforming FEM up-winding K. Georgiev, S. Margenov. Emission control in single species air pollution problems K. Georgiev et al. A new operator splitting method and its numerical investigation B.Gnandt. Advances in urban dispersion modelling S.-E. Gryning, E. Batchvarova. Internet-based management of environmental simulation tasks K. Karatzas. Air pollution assessment inside and around iron ore quarries M. Kharytonov et al. Data assimilation of radionuclides at small and regional scale M. Krysta et al. The impact of sea breeze on air quality in Athens area D. Melas et al. Developments and applications in urban air pollution modelling C. Mensink et al. Demands for modelling by forecasting ozone concentration in Western Slovenia A. Planinsek. A pilot system for environmental impact assessment of pollution caused by urban development and urban air pollution forecast I. Sandu et al. The use of MM5-CMAQ air pollution modelling system for real-time and forecasted air quality impact of industrial emissions R. San Jose et al. Regulatory modelling activity in Hungary R. Steib. Creation and testing of flux-type advection schemes for air pollution modeling application D. Syrakov et al. Bulgarian emergency response system: description and ensemble performance D. Syrakov et al. Global and regional aerosol modelling: a picture over Europe E. Vignati et al. The ABL models Yordan and Yorcon - top-down and bottom-up approaches for air pollution applications D. Yordanov et al. Major conclusions from the discussions Z. Zlatev et al. List of participants. Subject index.

Running an Advection-Chemistry Code on Message Passing Computers

Studying high pollution levels in different regions of Europe is an important environmental problem. Large mathematical models can successfully be used in the treatment of this problem. However, the use of large mathematical models in which all physical and chemical processes are adequately described leads, after the application of appropriate discretization and splitting procedures, to the treatment of huge computational tasks: in a typical simulation one has to perform several hundred runs, in each of these run one has to carry out several thousand time-steps and at each time-step one has to solve numerically systems of ODEs containing up to O(106) equations. Therefore, it is difficult to treat numerically such large mathematical models even when modern computers are available. Runs of an important module of a large-scale air pollution model on parallel message passing machines will be discussed in this paper. Numerical results will be presented.

Coupling the Advection and the Chemical Parts of Large Air Pollution Models

The discretization of long-range transport models leads to huge computational tasks. The advection (the transport due to the wind) and the chemistry are the most difficult parts of such a model. Normally splitting procedures are used and one tries to develop optimal methods for the advection part and for the chemistry part. Some results obtained in the attempts to design good sets of methods which work well for the coupled advection-chemistry sub-model will be presented. Runs on a Silicon Graphics POWER CHALLENGE computer indicate that the methods perform reasonably well and high speed-ups can be achieved with minimal extra efforts. However, more efforts are needed to get closer to the peak performance of this computer.

Studying absolute stability properties of the Richardson Extrapolation combined with explicit Runge-Kutta methods

Abstract Explicit Runge–Kutta methods are considered. It is assumed that the number of stages m , m = 1 , 2 , 3 , 4 , is equal to the order p of the selected method. The impact of the application of the Richardson Extrapolation on the absolute stability properties is studied. The Richardson Extrapolation was used until now only in an attempt to increase the accuracy of the numerical approximations or in order to keep the computational errors under some prescribed in advance level. Another issue, the absolute stability of the Richardson Extrapolation in connection with several numerical methods, is the major topic of this study. It is shown that not only are the combinations of the Richardson Extrapolation with explicit Runge–Kutta methods more accurate than the underlying numerical methods, but also their absolute stability regions are larger. This means that larger time-stepsizes can be used during the integration when Richardson Extrapolation is used. The validity of the theoretical results is confirmed by numerical experiments with three carefully chosen examples. It is pointed out that the application of Richardson Extrapolation together with explicit Runge–Kutta methods might be useful when some large-scale mathematical models, described by systems of partial differential equations, are handled numerically.

Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

The understanding of lakes physical dynamics is crucial to provide scientifically credible information foron lakes ecosystem management. We show how the combination of in-situ dataobservations, remote sensing observationsdata and three15 dimensional hydrodynamic (3D) numerical simulations is capable of deliveringresolving various spatio-temporal scales involved in lakes dynamics. This combination is achieved through data assimilation (DA) and uncertainty quantification. In this study, we presentdevelop a flexible framework forby incorporating DA into lakes three-dimensional3D hydrodynamic lake models. Using an Ensemble Kalman Filter, our approach accounts for model and observational uncertainties. We demonstrate the framework by assimilating in-situ and satellite remote sensing temperature data into a three-dimensional3Dl hydrodynamic 20 model of Lake Geneva. Results show that DA effectively improves model performance over a broad range of spatio-temporal scales and physical processes. Overall, temperature errors have been reduced by 54 %. With a localization scheme, an ensemble size of 20 members is found to be sufficient to derive covariance matrices leading to satisfactory results. The entire framework has been developed for the constraintswith a goal of near real-time operational systems and near real-time operations (e.g. integration into meteolakes.ch). 25

Numerical Methods and Applications

In this note we propose a grid refinement procedure for direction splitting schemes for parabolic problems that can be easily extended to the incompressible Navier-Stokes equations. The procedure is developed to be used in conjunction with a direction splitting time discretization. Therefore, the structure of the resulting linear systems is tridiagonal for all internal unknowns, and only the Schur complement matrix for the unknowns at the interface of refinement has a four diagonal structure. Then the linear system in each direction can be solved either by a kind of domain decomposition iteration or by a direct solver, after an explicit computation of the Schur complement. The numerical results on a manufactured solution demonstrate that this grid refinement procedure does not alter the spatial accuracy of the finite difference approximation and seems to be unconditionally stable.

Recursive Version of LU Decomposition

The effective use of the cache memories of the processors is a key component of obtaining high performance algorithms and codes, including here algorithms and codes for parallel computers with shared and distributed memories. The recursive algorithms seem to be a tool for such an action. Unfortunately, worldwide used programming language FORTRAN 77 does not allow explicit recursion.The paper presents a recursive version of LU factorization algorithm for general matrices using FORTRAN 90. FORTRAN 90 allows writing recursive procedures and the recursion is automatic as it is a duty of the compiler. Usually, recursion speeds up the algorithms. The recursive versions reported in the paper are some modification of the LAPACK algorithms and they transform some basic linear algebra operations from BLAS level 2 to BLAS level 3.

Efficient algorithms for large scale scientific computations: Introduction

Complex mathematical models are extensively used in our modern computer age to handle many difficult problems which arise in different fields of science and engineering. These models are typically described by time-dependent systems of partial differential equations (PDEs) and lead after appropriate discretization of the spatial derivatives to the solution of huge systems of ordinary differential equations (ODEs). The number of equations in these systems of ODEs is very often greater than one million. The discretization of the time derivative in the systems of ODEs leads to the treatment of algebraic equationswhich are as a rule also very large, non-linear and have to be handled by applying iterativemethods (very often the well-known quasi-Newton iterative procedure is used). Then huge systems of linear algebraic equations have to be solved during the iterative process. It should also be stressed that the mathematical models have normally to be run (1) many times, (2) on long time-intervals and (3) with different scenarios.

Application of Richardson extrapolation for multi-dimensional advection equations

Abstract A Crank–Nicolson type scheme, which is of order two with respect to all independent variables, is used in the numerical solution of multi-dimensional advection equations. Normally, the order of accuracy of any numerical scheme can be increased by one when the well-known Richardson Extrapolation is used. It is proved that in this particular case the order of accuracy of the combined numerical method, the method consisting of the Crank–Nicolson scheme and the Richardson Extrapolation, is not three but four.