# Finding Optimal Stations Using Euclidean Distance and Adjustable Surrounding Sphere
###### Abstract  
Air quality monitoring network (AQMN) plays an important role in air pollution management. However, setting up an initial network in a city often lacks necessary information such as historical pollution and geographical data, which makes it challenging to establish an effective network. Meanwhile, cities with an existing one do not adequately represent spatial coverage of air pollution issues or face rapid urbanization where additional stations are needed. To resolve the two cases, we propose four methods for finding stations and constructing a network using Euclidean distance and the k-nearest neighbor algorithm, consisting of Euclidean Distance (ED), Fixed Surrounding Sphere (FSS), Euclidean Distance + Fixed Surrounding Sphere (ED + FSS), and Euclidean Distance + Adjustable Surrounding Sphere (ED + ASS). We introduce and apply a coverage percentage and weighted coverage degree for evaluating the results from our proposed methods. Our experiment result shows that ED + ASS is better than other methods for finding stations to enhance spatial coverage. In the case of setting up the initial networks, coverage percentages are improved up to 22%, 37%, and 56% compared with the existing network, and adding a station in the existing one improved up by 34%, 130%, and 39%, in Sejong, Bonn, and Bangkok cities, respectively. Our method depicts acceptable results and will be implemented as a guide for establishing a new network and can be a tool for improving spatial coverage of the existing network for future expansions in air monitoring. E 2021 11  
comply with the Environmental Protection Agency (EPA) guideline or local government regulations [5]. Furthermore, various studies mainly consider pollution data, population density, land-use regression, distance to major roads, and high-risk observation regions to identify new air quality monitoring stations [6; 7; 8; 9; 10]. Some studies investigated pollution indicators in the area surrounding stations [11; 12; 13]. Such a zone is called a sphere of influence (SOI) and the original algorithm was developed by [PERSON] et al. in 1986. Their proposed method uses air pollution data to determine spatial coverage and the number of air monitoring stations [14]. Optimization, evaluation, and revision of existing AQMN to meet changing local area pollution levels has been an important research topic over the past few decades [15; 16; 17; 18]. The main cause regarding the distribution of air pollution and emission source changed caused by urbanization. The rapid expansion of the urban areas in developing countries of Asia leads to air quality monitoring issues such as excessive numbers of stations in urban regions and a lack of adequate numbers of stations in rural areas [19]. Consequently, several approaches have suggested adding or removing stations by considering various constraints such as population density, historical pollution data, terrain conditions, budget, and health impact. They use statistical analytics, weight criteria, holistic approaches, data simulation, and pure measurement for AQMN optimization [20; 21; 22]. Moreover, some studies apply terrain maps, heat maps, gridded synthetic assessment, and graphical information systems (GIS) to show high pollution concentration areas. They analyze pollution criteria and combine them with spatial statistics to determine suitable areas to recommend for station location sites [23; 24; 25; 26; 27]. However, studies of optimal designs or revision of AQMN in less developed countries (LDCs) are relatively scarce. Such studies in the literature are mostly related to minimizing air pollution's health impact [28; 29]. The LDCs have different issues than in developed countries, such as limited budgets to establish the stations, lack of historical pollution data, and requirements that demand air pollution monitoring cover vast areas. All of these constraints are critical factors for AQMN design [30].