Ph.D Thesis
Ph.D Student Nebenzal Asaf Mathematical Methods for Generating Accurate Dense Spatiotemporal Maps from Sparse Sensing Department of Applied Mathematics Professor Barak Fishbain

Abstract

Air pollution is one of the most prominent environmental health risks and pathogen generator. Many air pollution studies are based on data collected from air quality monitoring stations (AQMS). Yet, due to their high costs they are scattered sparingly. To cope this hurdle, AQMS data is generalized through mathematical methods. Here we present two new analytical methods for creating dense pollution maps in time and space from sparse sensing. These methods display unprecedented tools for air quality analysis and understanding. Specifically, long-term air quality forecasting is firstly introduced, then a method to compute it is implemented. A novel accurate interpolation scheme is also presented.  These methods lay the path for optimization-based analysis methodologies. To this end, a novel source term estimation method, which is a derivative of this work is presented.

While short-term forecasting, a few days into the future, is a well-established research domain, there is no method for long-term forecasting (e.g., the pollution level distribution in the upcoming months or years). Here we introduce and define long-term air pollution forecasting, where long-term refers to estimating pollution levels in the next few months or years. A Discrete-Time-Markov-based model for forecasting ambient NO2 patterns is presented. The model accurately forecasts overall pollution level distributions, and the expectancy for tomorrow’s pollution level given today’s level, based on longitudinal historical data. It thus characterizes the temporal behavior of pollution. The model was applied to five distinctive regions in Israel and Australia and was compared against several forecasting methods and was shown to provide better results with a relatively lower error rate.

Next, a novel, highly accurate method for producing dense air pollution maps, based on any given air-pollution dispersion model, is presented. The scheme consists of two phases. At the first stage the source locations and emission rates , as a function of the model’s parameter space are sought (“backward computation”). Then, the source term is used to generate the dense maps utilizing the same dispersion model (“forward computation”). The algorithm is model- invariant to the dispersion model, and thus is suitable for a wide range of applications. A simulation of an industrial area demonstrated that this method produced more accurate maps than current state-of-the-art.

One of the implications of those methods is developing a technique which deals directly with source term estimation. For this purpose, source term estimation using a sparse network of point sensors is presented. This method combined a dispersion model and self-adaptive multiobjective evolutionary search. The method searches for a set of leaks; each has a typical emission rate and location that will result in a minimal difference between the sensors actual and computed readings. This objective is balanced by a minimum number of active sources objective. The method was tested in a simulated 600m2 terrene with 0-9 sources. The results show that the method is effective, and the main limitation is the number of sensors and their spatial configuration.