تجزیه و تحلیل حساسیت مونت کارلو از یک مدل آلودگی هوا Eulerian در مقیاس بزرگ

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 ΛΠτΛΠτ 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.

Environmental security is a very important topic for the modern society. Development of reliable and sustainable mathematical models has a significant role at this area. Specification of the most influential factors (chemical rates, boundary conditions, emission levels) on model outputs using sensitivity analysis techniques already achieves valuable information for an improvement of the model and identification of parameters that must be studied more carefully. It will lead to an increase of reliability and robustness of predictions obtained by large-scale environmental and climate models. On the other hand, sensitivity analysis is a tool useful for all processes where it is important to know which input factors contribute most to output variability [1]. The aim of the present work is • to study the sensitivity of the concentration levels of important pollutants (like ozone O3) due to variation of chemical rates applying variance-based techniques for global sensitivity analysis and Monte Carlo approaches for numerical integration, • to compare the newly developed Monte Carlo algorithm based on Sobol's quasi-random points MCA-MSS [2] with some existing approaches, namely ○○ Sobol's ΛΠτΛΠτ sequences [3], ○○ adaptive Monte Carlo algorithm developed in [4] and [5], ○○ Sobol's sensitivity approach implemented in SIMLAB [6], ○○ eFAST sensitivity approach carried out via SIMLAB [6], and ○○ the plain Monte Carlo algorithm [3] and [4], • to show the superior efficiency of the sensitivity analysis methods proposed by the authors in [5], • to provide practical insights about the case study at hand, and • to try to provide operation guidelines on the estimation of relatively small Sobol's indices in the presence of computational difficulties. The input data for sensitivity analysis has been obtained during runs of a large-scale mathematical model for remote transport of air pollutants (Unified Danish Eulerian Model, UNI-DEM, 1 [7]). Among quantitative global sensitivity analysis methods, variance-based methods are the most often used [8]. The main idea of these methods is to evaluate how the variance of an input or a group of inputs contributes into the variance of model output. Two of the most often used variance-based methods have been applied—Sobol's approach and Fourier amplitude sensitivity test (FAST). The approaches have been implemented using a Monte Carlo algorithms (MCA) or SIMLAB software tool for global sensitivity analysis [6]. The results described here can be used for increasing the reliability of the mathematical model results, and identifying input parameters that should be measured more precisely.

The main contribution of the present paper consists in comparison analysis of a number of approaches for computing the sensitivity of the concentration levels of important pollutants due to variation of chemical rates. Variance-based techniques for global sensitivity analysis and Monte Carlo approaches for computing Sobol's sensitivity indices are used. Superior efficiency of the sensitivity analysis performed using the newly developed Monte Carlo algorithm based on Sobol's quasi-random points is shown. The obtained results have an important twofold role: for mathematical models verification and/or improvement, and/or for a reliable prediction the effects of high pollution levels (a) on human health and (b) on losses of crops in the agriculture. Most of the results can also be applied when other large-scale mathematical models are used. The analysis of various algorithm and numerical results show the following: • for smooth output relatively simple algorithms like plain Monte Carlo or quasi-Monte Carlo are efficient enough; • for non-smooth output with computational difficulties more complicated algorithms like adaptive Monte Carlo or MCA-MSS should be applied; • for relatively small sensitivity indices and non-regular output MCA-MSS is the most accurate approach.