Large-scale Air Pollution Model Research Articles

LARGE-SCALE AIR POLLUTION MODELING IN EUROPE UNDER DIFFERENT CLIMATIC SCENARIOS

The treatment of large-scale air pollution models is not only important for modern society, but also an extremely difficult task. Five important physical and chemical processes: (1) horizontal advection, (2) horizontal diffusion, (3) vertical exchange, (4) emission of different pollutants and (5) dry and wet deposition have to be united and handled together. This leads to huge computational problems which have to be treated on modern high-speed parallel architectures by using advanced numerical methods. The computational difficulties are vastly increased when such models are used in the investigation of the impact of climatic changes on high pollution levels that are often exceeding certain critical concentrations and, therefore, are becoming harmful for plants, animals and human beings. There are two major reasons for the great increase in computational difficulties: (a) it is necessary to run the discretized data on fine spatial grid models over very long time-periods consisting of many consecutive years and (b) different scenarios are to be used in order to investigate the sensitivity of the pollution levels to systematic variations of several carefully selected key parameters. How the major difficulties can be resolved is explained here. Furthermore, many results are presented in order to demonstrate the ability of the model to handle successfully the huge computational tasks by using fine space and time discretization and by applying a chemical scheme with many chemical species participating in several hundred chemical reactions. Our results indicate that the climatic changes will often lead to some increases in the pollution levels.

Relations between Climatic Changes and High Pollution Levels in Bulgaria

One of the important consequences of the climatic changes is the potential danger of increasing the concentrations of some pollutants, which may cause damages to humans, animals and plants. Therefore, it is worthwhile to study carefully the impact of future climate changes on the high pollution levels. The major topic of the discussion in this paper is the increase of some ozone levels in Bulgaria, but several related topics are also discussed. The particular mathematical tool applied in this study is a large-scale air pollution model, the Unified Danish Eulerian Model (UNI- DEM), which was successfully used in several investigations related to potentially dangerous pollution levels in several European countries. This model is described by a non-linear system of partial differential equations, which is solved numerically by using (a) advanced numerical algorithms and (b) modern computer architectures. Moreover, (c) the code is parallelized and (d) the cache memories of the available computers are efficiently utilized. It is shown that in Bulgaria, as in the other European countries, the climatic changes will result in permanent increases of some quantities related to the ozone pollution. The important issue is that in our study the changes of the dangerous pollution levels are followed year by year. In this way, an attempt is made both to capture the effect of the interannual variations of the meteorological conditions on the levels of the ozone concentrations and to follow directly the influence of the climatic changes on the pollution levels. Moreover, the sensitivity of the pollution levels to variations of the human made (anthropogenic) and natural (biogenic) emissions is also discussed.

On the Performance, Scalability and Sensitivity Analysis of a Large Air Pollution Model

Computationally efficient sensitivity analysis of a large-scale air pollution model is an important issue we focus on in this paper. Sensitivity studies play an important role for reliability analysis of the results of complex nonlinear models as those used in the air pollution modelling. There is a number of uncertainties in the input data sets, as well as in some internal coefficients, which determine the speed of the main chemical reactions in the chemical part of the model. These uncertainties are subject to our quantitative sensitivity study. Monte Carlo and quasi-Monte Carlo algorithms are used in this study.A large number of numerical experiments with some special modifications of the model must be carried out in order to collect the necessary input data for the particular sensitivity study. For this purpose we created an efficient high performance implementation SA-DEM, based on the MPI version of the package UNI-DEM. A large number of numerical experiments were carried out with SA-DEM on the IBM MareNostrum III at BSC - Barcelona, helped us to identify a severe performance problem with an earlier version of the code and to resolve it successfuly. The improved implementation appears to be quite efficient for that challenging computational problem, as our experiments show. Some numerical results with performance and scalability analysis of these results are presented in the paper.

Preparing input data for sensitivity analysis of an air pollution model by using high-performance supercomputers and algorithms

Sensitivity analysis is an important issue in large-scale mathematical modelling. We developed a novel 3-stage method for global sensitivity analysis of the Unified Danish Eulerian Model (UNI-DEM). This is a powerful large-scale air pollution model with an up-to-date high-performance software implementation. There is a number of uncertain internal parameters, especially in the chemistry–emission submodel, which are subject to our quantitative sensitivity study. Efficient Monte Carlo and quasi-Monte Carlo algorithms based on Sobol sequences are used in this study.A large number of numerical experiments with some special modifications of the model must be carried out in order to collect the necessary input data for the particular sensitivity study. For this purpose we created an efficient high performance implementation SA-DEM, based on the MPI version of the package UNI-DEM. A vast number of numerical experiments were carried out with SA-DEM on an IBM Blue Gene/P, the most powerful parallel supercomputer, at the time of the write-up of this paper, in Bulgaria. Even this powerful machine has some problems with the storage when SA-DEM is to be run with the refined (480×480) version of the mesh. The code was implemented with some enhancements on the IBM MareNostrum III at BSC — Barcelona, the most powerful parallel supercomputer in Spain. This implementation appears to be quite efficient for that challenging computational problem, as our experiments show. Some numerical results and performance analysis of these results will be presented in the paper.

Spline interpolation for modelling of accumulated effects of ozone

An alternative approach for computing exposure indices, such as AOT40 of the ground-level ozone, is considered in this paper. The aim of the study is to compare it with the traditional way of calculating the exposure indices in order to discover possible weaknesses or strengths of both approaches. The problem under consideration is of great importance when modelling results, obtained after running large-scale air pollution models, have to be compared with experimental data. Usually the data are received in a form of mesh-function. At the same time, accumulated effects have to be considered as integrals of smooth (at least continuous) functions. Cubic spline interpolation over data of ozone concentrations is considered as a tool for computing accumulated effects. Practical computations include estimations for measurements of several stations over Europe for two different years. The results obtained with the proposed procedure are compared with those achieved from the calculations according to the classical definition.

Advanced algorithms for multidimensional sensitivity studies of large-scale air pollution models based on Sobol sequences

In this paper advanced variance-based algorithms for global sensitivity analysis are studied. We consider efficient algorithms, such as Monte Carlo, quasi-Monte Carlo (QMC) and scrambled quasi-Monte Carlo algorithms based on Sobol sequences. Low discrepancy ΛΠτ Sobol sequences are considered as a basis. Two other approaches are also analyzed. The first one is an efficient Monte Carlo (MC) algorithm for multidimensional integration based on modified Sobol sequences (MCA-MSS) and proposed in an earlier work by some of the authors Dimov and Georgieva (2011) [28]. The second one is a randomized QMC algorithm proposed by Art Owen (1995) [20]. The procedure of randomization in the latter case is also known as Owen scrambling.The algorithms considered in this work are applied to sensitivity studies of air pollution levels calculated by the Unified Danish Eulerian Model (UNI-DEM) to some chemical reaction rates. UNI-DEM is chosen as a case study since it constitutes a typical large-scale mathematical model in which the chemical reactions are adequately presented. Extensive numerical experiments are performed to support the theoretical studies and to analyze applicability of algorithms under consideration to various classes of problems. Conclusions about the applicability and efficiency of the algorithms under consideration are drawn.

Monte Carlo sensitivity analysis of an Eulerian large-scale air pollution model

Variance-based approaches for global sensitivity analysis have been applied and analyzed to study the sensitivity of air pollutant concentrations according to variations of rates of chemical reactions. The Unified Danish Eulerian Model has been used as a mathematical model simulating a remote transport of air pollutants. Various Monte Carlo algorithms for numerical integration have been applied to compute Sobol's global sensitivity indices. A newly developed Monte Carlo algorithm based on Sobol's quasi-random points MCA-MSS has been applied for numerical integration. It has been compared with some existing approaches, namely Sobol's ΛΠτ sequences, an adaptive Monte Carlo algorithm, the plain Monte Carlo algorithm, as well as, eFAST and Sobol's sensitivity approaches both implemented in SIMLAB software. The analysis and numerical results show advantages of MCA-MSS for relatively small sensitivity indices in terms of accuracy and efficiency. Practical guidelines on the estimation of Sobol's global sensitivity indices in the presence of computational difficulties have been provided.

Air pollution modelling, sensitivity analysis and parallel implementation

A new approach for Sensitivity Analysis (SA) in the field of air pollution modelling is proposed and applied to the Unified Danish Eulerian Model (UNI-DEM), a large-scale air pollution model. The SA requires numerous model experiments with different values of the studied parameters. By simultaneous variation of these parameters we produce a set of multidimensional discrete functions. These huge computational tasks require extensive resources of storage and CPU time. A highly parallel implementation of UNI-DEM has been created for this purpose and implemented on two powerful supercomputers. Some details of this implementation and numerical results on these supercomputers are presented.

Stability of the Richardson Extrapolation applied together with the [formula omitted]-method

Consider a system of ordinary differential equations (ODEs) d y / d t = f ( t , y ) where (a) t ∈ [ a , b ] with b > a , (b) y is a vector containing s components and (c) y ( a ) is given. The θ -method is applied to solve approximately the system of ODEs on a set of prescribed grid points. If N is the number of time steps that are to be carried out, then this numerical method can be defined using the following set of relationships: y n = y n − 1 + h ( 1 − θ ) f ( t n − 1 , y n − 1 ) + h θ f ( t n , y n ) , θ ∈ [ 0.5 , 1.0 ] , n = 1 , 2 , … , N , h = ( b − a ) / N , t n = t n − 1 + h = t 0 + n h , t 0 = a , t N = b . As a rule, the accuracy of approximations { y n ∣ n = 1 , 2 , … , N } can be improved by applying the Richardson Extrapolation under the assumption that the stability of the computational process is preserved. Therefore, it is natural to require that the combined numerical method (Richardson Extrapolation + the θ -method) is in some sense stable. It is proved in this paper that the combined method is strongly A-stable when θ ∈ [ 2 / 3 , 1.0 ] . It is furthermore shown that some theorems proved in a previous paper by the same authors, Faragó et al. (2009) [1], are simple corollaries of the main result obtained in the present work. The usefulness of the main result in the solution of many problems arising in different scientific and engineering areas is demonstrated by performing a series of tests with an extremely badly scaled and very stiff atmospheric chemistry scheme which is actually used in several well-known large-scale air pollution models.

Adaptive Monte Carlo Algorithm for Sensitivity Studies of Eulerian Large-scale Air Pollution Models

Sobol’ global sensitivity indices have been used here as main numerical indicators for sensitivity of model output to input parameters. Therefore the basic mathematical problem is computing of multidimensional integrals. Numerical results for an Eulerian large-scale air pollution model have been presented. They have been obtained by using an adaptive Monte Carlo algorithm for numerical integration. The results have been compared with SIMLAB implementation of applied approaches for sensitivity analysis.

Different splitting techniques with application to air pollution models

Splitting techniques are commonly used when large-scale models, which appear in different fields of science and engineering, are treated numerically. Four types of splitting procedures are defined and discussed. The problem of the choice of a splitting procedure is investigated. Several numerical tests, by which the influence of the splitting errors on the accuracy of the results is studied, are given. It is shown that the splitting errors decrease linearly when (1) the splitting procedure is of first order and (2) the splitting errors are dominant. Three examples for splitting procedures used in all large-scale air pollution models are presented. Numerical results obtained by a particular air pollution model, Unified Danish Eulerian Model (UNI-DEM), are given and analysed.

Testing the accuracy of a data assimilation algorithm

Variational data assimilation techniques have been successfully used in connection with comprehensive research projects in different fields of science and engineering. The use of the variational data assimilation approach is becoming more and more popular also in the attempts to improve the accuracy of the results obtained by running large-scale air pollution models. Different tests were carried out in order both to check the ability of the data assimilation procedures to improve the initial concentrations and to start building up a benchmark for testing the performance of these procedures on different modern high-speed computers. Selected results from these tests will be presented and discussed in this paper.

Parallel runs of a large air pollution model on a grid of Sun computers

Large-scale air pollution models can successfully be used in different environmental studies. These models are described mathematically by systems of partial differential equations. Splitting procedures followed by discretization of the spatial derivatives lead to several large systems of ordinary differential equations of order up to 80 millions. These systems have to be handled numerically at up to 250,000 time-steps. Furthermore, many scenarios are often to be run in order to study the dependence of the model results on the variation of some key parameters (as, for example, the emissions). Such huge computational tasks can successfully be treated only if: (i) fast and sufficiently accurate numerical methods are used and (ii) the models can efficiently be run on parallel computers. The mathematical description of a large-scale air pollution model will be discussed in this paper. The principles used in the selection of numerical methods and in the development of parallel codes will be described. Numerical results, which illustrate the ability of running the fine resolution versions of the model on Sun computers, will be given. Applications of the model in the solution of some environmental tasks will be presented.

Performance results of a large-scale air pollution model on two parallel computers

The size of the computational task obtained after the appropriate splitting and discretisation procedures of the system of partial differential equations in large air pollution models is enormous. Even when computers with several GFLOPS top performance are in use, it is difficult to solve this problem efficiently and, furthermore, to prepare codes that can be used for operating purposes. Some performance-comparison results obtained by runs of the parallelised via MPI unified variable-grid version of the Danish Eulerian model for long-range transport of air pollutants on two parallel computer architectures are presented. The test numerical experiments are performed on a Beowulf-like cluster set-up of four two-processor Macintosh G4 machines and a multiprocessor SUN (up to 32 processors). The Message Passing Interface (MPI) standard is used on both distributed and shared memory parallel computer platforms. Timing results, speed-up and parallel efficiency of the main computational stages as well as of the whole model are presented.

Parallel matrix computations in air pollution modelling

Mathematical models for large-scale air pollution studies consist of systems of partial differential equations (PDEs). The number of equations in these systems of PDEs is equal to the number of chemical compounds (the number of chemical compounds involved in the current large-scale air pollution models varies from 20 to about 200). The space domain of the systems of PDEs is normally very large, because the models must be able to treat transboundary long-range transport of the harmful pollutants. The time-intervals are often very long (runs with meteorological data covering up to 10 years have sometimes to be carried out). Moreover, fine spatial and temporal resolution is as a rule required. This leads to very large computational tasks when the air pollution models are discretized. Therefore, it is necessary to use fast and sufficiently accurate numerical methods as well as to exploit efficiently the great potential power of the parallel computers. Some results, which are obtained when several versions of a large-scale air pollution model are run on different parallel architectures, will be presented in this paper.

Numerical treatment of large-scale air pollution models

Studying air pollution phenomena over a large space domain by a fairly general mathematical model is discussed. The space discretization of such a model leads to huge system of ODEs. The integration algorithm used in the solution of these systems must be efficient. If a 3-D model is considered, then a vector processor is to be used. Moreover, the most time-consuming parts of the code are to be vectorized. The calculated results, concentrations of different air pollutants, must be reliable, because they have to be used by other specialists. Therefore different checks concerningthe reliability of the results are carried out. In this paper it is shown that an efficient and reliable code for studying both sulphur and nitrogen pollution has been developed at the Danish Agency of Environmental Protection. Some simulation processes are also described breifly.