Spatial distribution of public elementary schools: a case study of Najran, Saudi Arabia

ABSTRACT Spatial equity in the provision of educational services is a major component to provide a healthy and cheerful living environment in cities. Experts, accordingly, set many standards for selecting school locations. This study has used many of those standards to investigate the spatial distribution of boys’ public elementary schools in Najran city. Statistical techniques such as Locational Quotient, Lorenz Curve, and Geographic Information System tools were employed to show the spatial distribution and analysis of elementary schools. In addition, GIS evaluates the current locations of schools and suggests suitable locations for future schools. The results indicate that the population number and schools within the city are not equidistributed. Some districts are experiencing a glut and concentration of schools, especially in old, fully developed, and highly populated districts, while most of the new eastern districts suffer a lack and have no adequate access to schools. Also, half of the city districts do not have elementary schools. Furthermore, many schools are located close to sources of danger or nuisance sources. Consequently, the study concluded by showing suitable locations for future schools and recommended that planners provide elementary schools in deficient districts and enhance equitable distribution of elementary schools throughout the city. GRAPHICAL ABSTRACT


Introduction
In recent decades, overpopulation growth and increasing urbanization in many developing countries have put excessive pressure on city services (Wazzan 2017). In many cases, the capacity of existing services cannot meet the increased demand of the population, especially in the absence of pre-planning for the number and the distribution of services (Cohen 2006;Wu et al. 2020a). This necessitates the intervention of planners and decision-makers to take the required measures to provide the efficient and high-quality public services that residents are looking for in terms of amount and adequate spatial distribution (Carvalho, 2010;Cohen 2006) One of the most essential public services that residents need on a continual basis is educational services, which are important to any city's population. Many countries around the world have created systems and policies to achieve educational equity. Assessing the efficiency of educational service is a multidimensional task that includes many factors such as availability, quality, quantity, distribution, geographic and financial accessibility, and client satisfactions (Dawod et al. 2013). Nevertheless, the spatial distribution of schools is the most important factor. Urban planners are responsible for the equitable spatial distribution of schools within the cities so that schools can cover the current and targeted population, thus allowing students to go to schools safely, with the lowest cost and effort in terms of time and distance. Besides that, school locations should follow the standards of distance from desirable (e.g., parks) and non-desirable land uses (e.g., factories) (Al-Meteer 1999;General Directorate of Military Survey, 2002). However, many public services in general, and schools in particular, are placed rather haphazardly; at many locations and times, sites are undertaken according to need (Al-Zeer 2005). Therefore, the spatial analysis of school distribution has gained increased attention in the last few decades from an urban planning, geographical, and environmental perspective (Elzahrany 2003). They have been trying to achieve what is called spatial justice (Dadashpoor and Rostami 2011).
In order to evaluate and analyze the spatial distribution of public elementary schools in Najran city, Saudi Arabia, this study tries to assess the relationship between the spatial distribution of boys' elementary schools and population distribution through some statistical techniques. Then, it will rely on the construction of geographical information systems (GIS) that many studies concerning educational services adopt as a technical tool for analyzing and evaluating the spatial distribution and network, measuring accessibility, and managing and presenting data related to educational facilities (Alrasheed and Elgamily 2013;Dawod et al. 2013). This study also provides suggestions for educational service agencies about current and future suitable locations in Najran or another city with similar characteristics.

The problem statement
Throughout the last four decades, many educational changes have occurred in Saudi Arabia; the implementation of the five-year development plans that began in the early 1970s was the main driving force behind these changes (Al-Zeer 2005). Most Saudi cities have witnessed major rapid changes in land use, urban development, and population growth, resulting in more pressure on existing educational services (Belarem et al. 2018). As a result of these changes, many issues have arisen. One of these issues is how the schools' sites are chosen (Alrehili 2015). No systematic way was used to select many school locations, despite having established standards, leading to some common concerns. For instance, many schools in the Saudi cities have been placed by highways or congested roads or are in proximity to dangerous or nuisance sources; another problem is that some neighborhoods have clustered public elementary schools while others lack schools (Alharbi 2018;Alrehili 2015). In addition, it is common in Saudi Arabia that the residents of a small village or a district may convince decision-makers to establish a new school even if their request is not justifiable (Al-Zeer 2005).
Therefore, this paper tries to detect the spatial degree of inequality and adequacies in the provision of boys' public elementary schools in Najran and whether the schools' locations are chosen based on the standards, whether they are distributed randomly or follow a specific pattern, and whether they cover all populated neighborhoods. To achieve this aim, the author examines the spatial evolution of elementary schools' current system in terms of number and locations, patterns, density, and proximity to desirable or non-desirable land use, then evaluates the spatial distribution and suggests suitable locations for future schools. However, this study only focuses on boys' public elementary schools and does not cover girls' public elementary schools due to the lack of spatial and statical data about girls' schools; additionally, girls' schools are served by an organized, timely, accurate, and safe school bus network.

The significance of the study
This study is important since it is the first study in Saudi Arabia using statistical and spatial techniques to address the spatial distribution of public elementary schools in Najran and tries to find out whether the distribution of boys' elementary schools is based on acceptable standards related to educational service distribution. Also, this study investigates the relationships between school locations and the surrounding and impactful desirable and non-desirable land uses. This study is a unique one since it evaluates the current locations of schools and suggests suitable locations for future schools. Additionally, this study tries to fill in some gaps in the theory and literature review of urban education spatial distribution in developing countries. Eventually, the results of this study should shed light on several essential issues related to the locations of this type of school. Finally, the study's contributions can serve as a point of reference for research regarding the spatial distribution of schools in developing countries in general and Saudi Arabia in particular.

Literature review
Urban planning and geography fields have become a major contributor to solving the population's everyday problems, especially when practitioners choose the most appropriate public services locations (Al-Sheikh 2010). Planners can choose the most suitable sites for public services by understanding the relationship between humans, the environment, and land uses within the city or region; furthermore, they study phenomena distribution and whether the distribution constitutes a specific pattern or is random. So, suppose the distribution constitutes a particular pattern; in this case, it means there are some factors behind the formation of this pattern that the researchers seek to find and understand, but if the distribution is random, this indicates the weakness of the accuracy that created this pattern (Haggett 1979).
The geography of education is defined by Kučerová and Kučera (2012) as "a scientific discipline consisting of the study of spatial variations in the provision, uptake, and output of educational facilities and resources." They also added that when inequality exists in a city, urban planners and geographers need to examine the differences in school distribution across the city or region. Malczewski and Jackson (2000) show that schools must be organized in such a way to maximize accessibility to those within a school district; they explained that the equity concept could be achieved through minimizing the variability of the access to schools. In other words, spatial equity in educational services is the expectation of human beings for the distribution of public service facilities, including providing convenient and quick access to educational facilities; all students should be treated equally (Wu et al. 2020b). In addition, the same space separation should exist between all educational facilities and population residents (Rosa 2014). Therefore, one of the factors to evaluate spatial equity is accessibility (Tsou, Hung, and Chang 2005), and this is mainly based on physical distance measurements (Hewko, Smoyertomic, and Hodgson 2002;Fan et al. 2017). However, this factor is often impractical since it ignores many other indicators such as proximity to other land uses, service scope, construction of the buildings, road network structure, and population density. Thus, many scholars introduced some other factors that can evaluate the quality of facilities, such as service range and size (Tsou, Hung, and Chang 2005), population differences among different locations (Chang and Liao 2011), funding, since it can improve the quality of schools (Adams 1994), teacher-student ratio (Rodriguez and Elbaum 2014), and the school building construction (Earthman 2017). However, in this study, the concentration will be on the equity of the spatial distribution of schools and the factors affecting it.
Al-Awadhi and Mansour (2018) defined spatial inequity as the variation among geographic zones regarding the distances from home to the desired service facility, such as a school or hospital. Zenk, Tarlov, and Sun (2006) added that spatial inequity describes how service facilities are not distributed evenly throughout the specific area. Therefore, it can be an interpretative method of analyzing imbalance and unequal allocation of services across a geographic area (Barbieri et al. 2019). According to the geographic theoretical basis, the spatial equity or spatial justice of desirable public services such as schools means a shorter distance between residents and the public services; in other words, the public services are in reach and they are not unevenly distributed over the space. However, the distance to non-desirable services such as landfills and factories should be longer, so the population is not affected (Al-Awadhi and Mansour 2018). On the other hand, some authors asserted that the concept of spatial justice does not have a clear definition. It features the role of space in producing justice and injustice (Williams 2013). Also, Barbieri et al. (2019) added that if spatial justice is a spatially dependent issue, it cannot be determined only through traditional indicators at an administrative level but also through diverse aspects of socioeconomic, demographic, and social factors of the residents, as well as the differences and similarities from one location to another.
Studies of the spatial distribution of elementary schools in western countries began as early as 1929 when Clarence Perry devised the famous theory of the "neighborhood unit" where the elementary school is located in the neighborhood center with a maximum one-quarter mile distance for pupils walking to school. Then, in the 1950s, scholars began to study school district deviation and location planning to understand social impacts and other factors, rather than just economic factors. This can be called "location theory" (Yan et al. 2018). Furthermore, the interest in studying spatial distribution of schools began in the early 1960s, but many studies found problems associated with school locations.
Selecting the appropriate location for schools is a significant factor for authorities responsible for the spatial equity of schools. The location, size, and proximity to positive or negative externalities can materially affect pupils' educational achievements. Thus, many agencies responsible for education have developed selection site criteria not only for current needs but also for projected needs. For example, UNESCO (1985) issued norms and standards for the selection of prospective school sites, with the main factors being: the school must not be located in front of railways or major roads; the location must be more than 200 m from noisy and noxious industries and more than 400 m to the leeward of factories; students will not have to cross dangerous roads; the land is level and well-drained; availability of water and other services; and easy access to a playing field.
In the U.S.A., selection criteria were also developed by agencies. For example, the important criteria of the California Department of Education CDE (2004) are: there should be safe sidewalks and bike lanes to the school, especially within the walking or biking distance to schools (½ mile); the school site should not be subject to flooding, and the maximum noise in the area surrounding schools is 50 decibels. The distance to the closest airport runway should be at least 3.2 km, 100 m to power transmission lines, 400 m to hazardous air emissions or handled hazardous materials or wastes, 450 m to major roads, railroad tracks, and aboveground or underground pipelines that can pose a safety hazard (e.g., pressurized gas, gasoline, sewer, high-pressure water pipelines). Furthermore, the U.S. Environmental Protection Agency [EPA] (2011) issued some standards such as the accepted maximum walking or biking distance is a ½ mile (800 m) to the closest elementary school; walking distances should be less than a ½ mile to the community facilities (e.g., libraries, parks, museums). The distance to hazardous waste sites, landfills, and solid waste should be more than 1 mile (1.6 km); a ½ mile (800 m) to high-traffic roads and highways, rail lines, and large industrial facilities; 300 m to gas stations and other fuel-dispensing facilities and small sources (e.g., auto body shop, furniture, wood, electronic manufacturing); 3.2 km to the airport runway; 150 m to power lines; 450 m to hazardous material pipelines and water or fuel storage tanks; and 400 m to geologic hazards (e.g., landslide zone, volcanic activity, flood zone).
In Saudi Arabia, the government took into consideration the importance of improving education quality, and it considered that implementing planning standards for selecting schools' sites is an important tool for achieving the goals of their development strategies. Therefore, the government commissioned many relevant government agencies to set the standards, such as the Ministry of Municipal and Rural Affairs (MOMRA), General Directorate of Military Survey (GDMS) (Zabedi 2010), and Riyadh Municipality.
MOMRA sets standards for selecting elementary school sites, and they include: each school serves a neighborhood (3,600 residents); the service buffer zone is 500 m; all students can reach the school walking on safe sidewalks or local streets; the site should be away from noise, pollution, dust, and natural hazards; and it is preferable to be in proximity to a park (MOMRA 2006). GDMS (2002) also sets standards for selecting elementary school locations, although this agency is not related to the education field. Those standards are: the elementary school should be 500 m away from another elementary school; 150 m from the closest highway or main road; 75 m from the nearest road intersection or gas station; 3 km from the closest airport; 150 m from power transmission lines and 500 m from any power transmission plant; 150 m from factories and warehouses; 1 km from cooking gas cylinder distributors or hazardous materials warehouses and factories; 300 m from valleys; 100 m from water catchment areas; and the land slope must be less than 18%. Riyadh Municipality (2001) issued a guideline for educational services. There should be an elementary school for boys and another for girls for each 3,600 population and it should be connected to students' homes by safe sidewalks. The buffer zone for each elementary school is 550 m, where students can walk to school easily; it should be far away from noisy and congested streets.
The selection criteria can help the responsible team to select proper locations that provide a safe and supportive environment for instructional programs and the learning process. However, many elementary schools do not follow these criteria, since many are located in improper locations. For example, they are either located immediately beside highways, next to a congested road intersection, or in proximity to noisy factories or a valley.
In Riyadh city, the capital of Saudi Arabia, Alquraini (2001) found that 104 out of 167 wards did not have schools, and most of those schools were distributed in a convergent way. In addition, the author found that the distance between homes and schools varied between 1 to 25 km. Similarly, the study by Al-Zeer (2005) revealed a shortage of schools in the north part of Riyadh, resulting in overcrowding in most schools. Regarding the spatial distribution of schools in northern Riyadh, Alharbi (2018) also concluded that the distribution of schools takes a clustered pattern heading towards randomness; this pattern is characterized by the concentration of schools around one another in a small area and buffer zones of schools overlapping between many schools, while other areas had a shortage. Regarding proximity to the danger area, Al-Meteer (1999) found that 42% of schools in Riyadh were located next to unsafe roads.
In Jeddah, the second-largest city in Saudi Arabia, many studies were conducted to examine schools' spatial distribution. Belarem et al. (2018) and Zabedi (2010) concluded that schools' spatial distribution showed a great imbalance between the districts; many schools were concentrated in the city center, where the population density is greater, while the north and south districts had few schools. This distribution was relatively proportional to the distribution of population numbers and densities. However, a large proportion of residents had problems with accessibility to schools, and it became more difficult with the weak network of school buses and public transportation services. Zabedi (2010) added that most of the schools in Jeddah were clustered in some wards, especially areas with high population density; also, based on MOMRA and GDMS standards, buffer zones of schools overlapped between many schools. School site selection did not follow set standards; some were located close to main roads, gas stations, or noisy areas. Pasha (2004) showed that 4.5% of elementary schools were located next to main roads, and around 34% of the schools were near collector streets. Recent work by Murad, Dalhat, and Naji (2020) investigated the location distribution and accessibility of the elementary schools in Jeddah, and the authors found a shorter commuting distance to denser schools that are mainly located in the center of the city while other districts of the city need more schools.
In Makkah, Alrehili (2015) evaluated the current locations of schools and the results showed that many schools did not follow school site selection standards; they were located in certain districts only while others lacked schools, and many were in proximity to dangerous land uses. On the other hand, Dawod et al. (2013) found a strong positive relationship between the number of schools and population density. However, the city still needed many schools to cover the shortage in some districts. In Abha, Alhajri (2016) found that schools were clustered in districts near the city center and western districts where the population density is higher, and most schools were distributed randomly. Similar results were also found by Alqahtani (2018), and he added that the city is still in need of many elementary schools since the current schools only cover 8% of the Abha area.
In some cities in Saudi Arabia, only one study was found which dealt with the schools' distribution within the city, such as Buraidah, Hail, and Najran. For example, Alsagri and Aldagheiri (2013) examined the equity in the spatial distribution of schools in Buraidah city and found that schools were unevenly distributed, with many schools concentrated in wards near the city center. Also, there was a positive relationship between the number of schools and population density. In Hail, Hail Region, the results of Alshammari's (2011) study revealed that schools followed a randomly dispersed pattern, and some highly populated districts were not covered by schools. The only study in Najran was done by Alsalem (2011), and it was designed to analyze the equity of spatial distribution in schools when the city had forty-six districts and before the planning of the eastern districts located near Najran University. This study used questionnaires and interviews to measure the accessibility to schools. The results showed that schools were distributed among only thirtyfive districts within the city, with a dispersed distribution that tended to be random; 70% of the students suffered from walking a long distance to schools, and 42% of students pointed out that they cross a highway or main roads during their walk. However, there was a positive relationship between the schools' numbers and the population density of the districts.
Most of the previous studies used GIS techniques to investigate the spatial distribution of schools within cities; however, very few studies were found using Location Quotient (LQ) and Lorenz Curve. For example, Wazzan (2017) studied the spatial degree of inequality in the provision of the first and second stage of basic education schools in Lattakia, Syria, and the results revealed that the population and the number of schools are not equidistributed since schools are concentrated in some districts while other lack schools. LQ values are different between both types of schools, where it is from 0 to 2.54 for the first stage and from 0.60 to 1.94 for the second stage; this means as the number increases above one, the schools become more concentrated. The results of the Lorenz Curve showed that about 50% of first-stage schools are enjoyed by around 50% of the residents, and 50% of the second-stage schools are enjoyed by 60% of the residents. Another study by Musa and Mohammed 2012) in Bida City, Nigeria, investigated the schools' distributions and found that schools were not guided by population distribution in the districts. The LQ for elementary schools varied between 0-6.8 and 0-27.2 for high schools, which means some districts are deficient in elementary schools, and some of the populations did not have adequate access to these facilities.
From studying the school site selection standards and previous studies, it is found that in Saudi Arabia, some agencies who are not responsible for educational services have issued some standards, while the Ministry of Education or any of its branches have not issued any published guidelines. Also, it is found that many existing standards either nationally or internationally did not cover most aspects and distances related to suggested school locations, except for EPA and GDMS standards that consider many criteria in detail and proper distances to surrounding elements or land uses. In addition, inequity in the spatial distribution of schools is visible in most schools in Saudi cities. Most schools were clustered in the city center districts, where there is a higher population density and lower vacant lands, whereas distant districts of the city center -especially the new districts with few population densities -lack schools. Many schools are also located in proximity to danger or nuisance sources that negatively affect educational achievements.
Parts of the studies mentioned in the literature support this study in terms of the examined educational service and its goals. They aimed to examine the equity in the spatial distributions of schools, search for inappropriate distribution and amend it, examine the proximity to desirable and non-desirable land used, and choose suitable locations for schools. Therefore, this study benefits from the standards and previous studies in support of the theoretical side, determining the appropriate methods for the study and using the statistical and GIS techniques to produce and analyze the maps.

Methodology and data processing
This study utilizes the quantitative methods related to the statistical and spatial analytical approach, which could help recognize the spatial distribution of elementary schools in different locations within the city and highlight the spatial differences in the distributions (Meselhi 2008). So, in the next processing stage, the equity issue of elementary schools' distribution with respect to population has been investigated. In this regard, the author utilized Location Quotient (LQ), Lorenz Curve, and the ratios and percentages. This is followed by using a unique tool, GIS, to analyze and display geographically referenced information.
First, the Location Quotient (LQ) shows the extent of spatial concentration or inequity of elementary schools in the districts, and it can be computed by using equation (1). The LQ of each district is expected to be 1.0. However, if the value is greater than 1.0, it means that the district has a higher concentration of elementary schools than the city. LQ X; A ð Þ ¼ Another method is the Lorenz Curve, which is widely used in urban planning and geography to measure the equality distribution through a diagonal line where the greater the deviations of the Lorenz Curve means the greater the inequality. In contrast, zero means complete equality, and 1 means complete inequality. By putting the cumulative proportion of elementary schools in the y-axis and the proportion of the population in the district on the x-axis, the area of equality is being calculated. Besides that, ratios and percentages are used to explain the relationships between some variables, such as the ratio of schools to the population by the district.
In the last two decades, GIS school mapping has often been used for educational planning (Burrough et al. 2015); it provides a mapping tool for the relationships between school distribution, different surrounding land uses, and age of the population, and it is an efficient tool in managing and planning the accessibility to schools (Hite 2006). As stated by Yan et al. (2018), GIS technology has been widely used in studies related to education facilities' spatial distribution since the 1980s and is demonstrated in many of the previous studies such as (Alharbi 2018;Alqahtani 2018;Al-Zeer 2005;Zabedi 2010). This technology contributes to reaching accurate and fast statistical results for the distribution of geographical phenomena, such as the spatial distribution of elementary schools, through creating a spatial and descriptive database which can help to find the relationship between school locations and the surrounding and influencing geographical phenomena and to determine their patterns and characteristics in a way that traditional methods are incapable of (Dawod 2012). In addition, GIS technology can also be used in choosing future suitable school sites (e.g., Alqahtani 2018; Alrehili 2015; Zabedi 2010) or redistributing some of the current schools (e.g., Alharbi 2018;Alrehili 2015).
In this study, first, GIS is used to show the schools' numbers, locations, and density per district and population in the maps provided by Najran Municipality. Then, some important spatial tools available in GIS are used to measure the spatial geographic distributions. These methods measure and compare school distribution by calculating the values that represent the characteristics of distribution such as concentration, dispersion, and directions (Esri 2020a); these methods are also known as measures of spatial dispersion and spread, and they include, for example, mean center, central feature, standard distance, and directional distribution, which are explained in detail in the analysis section.
The third GIS tool used is the density analysis tool, which can determine the extent of density change of the phenomenon distribution throughout the study area (Dawod 2012). It has two major techniques, point density and kernel density, which are explained and used below. Fourthly, analyzing patterns is an incredibly effective method in revealing elementary schools' distribution patterns and showing whether they have a specific pattern or are distributed randomly. Analyzing patterns has some techniques that help find the spatial distribution type of elementary schools, such as nearest neighbor analysis, Ripley's K function, and Moran Index. This is followed by using GIS proximity tools that show the extent of the phenomenon's proximity to similar geographic variables, desirable and non-desirable land uses. The major techniques in proximity tools are buffer zone, point distance, and Thiessen polygons; those techniques are discussed and used in the results section. The sixth important GIS method is the spatial interpolation that predicts values for cells in a raster form for a limited number of sample data points (Esri 2020b). The most important techniques in spatial interpolation that can show the concentration or higher and lower density of schools are Inverse Distance Weighted (IDW) and kriging. Additionally, a GIS tool that determines the statistically significant spatial clusters of high values (hot spots) and low values (cold spots) is used, and it is called hotspot analysis.
Finally, some GIS techniques are used to examine the suitability of current school locations and suggest proper future elementary school locations. The reference standards for all of the processes are mainly CDE, EPA, MOMRA, GDMS, and Riyadh Municipality; those standards assist in examining whether elementary school sites in Najran were chosen based on the standards or not, especially in terms of the spatial distribution pattern, coverage of the population, density, and proximity to desirable and undesirable land use; those standards also help to suggest prospective suitable boys' elementary school sites.
In this study, the directional hypothesis is used, and it is a prediction made by the author regarding the relationships between two variables. So, the main hypothesis is that all boys' elementary schools are distributed equally within the city districts. Also, one would assume that each district has at least one elementary school; in addition, one would hypothesize that in a district of a greater number of populations, we would observe more elementary schools within that district. In other words, there is an elementary school for each 3,600 population as requested by the standards. Furthermore, it is assumed that boys' elementary schools are located within 500 m of students' residences. Regarding choosing elementary school locations, it is hypothesized that schools follow the standards of school site selection, which have been set by authorities regarding the distances from other elementary schools and desirable or non-desirable land uses.

Study area
Najran city is located in the southwestern part of Saudi Arabia, as shown in Figure 1 (General Authority for Statistics [GASTAT], 2010). This city has a stripe shape in a flat land, and its area is about 885 km 2 ; the city has seventy-eight residential districts, as shown in Figure 1) (Najran Municipality 2019). The population number of Najran increased sharply; it was 192,325 inhabitants in 1992 (GASTAT 1992), and the number increased by more than double to 454,035 inhabitants 1 in 2019 (Najran Municipality 2019). This may be due to the increase in immigration rates to Najran, especially after the opening of Najran University, the high rates of investment in the city, and the increased financial allocations directed to the city.
In Najran, the average population density in 2019 varied between districts of the city; it is higher in proximity to the city center and some old districts, which was around 174 inhabitants/hectare, and then, it declined to about forty-eight inhabitants/hectare in further districts. It decreases to less than five inhabitants/hectare in half of the city's districts, especially the city's eastern districts, as shown in Figure 1) (Najran Municipality 2019). Regarding the number of boys' elementary schools, in 1965, there were only four elementary schools in Najran; however, the number increased to fifty-three schools by 2019 (Ministry of Education 2020).

Results and discussions
The data and maps of elementary school locations within Najran districts help to interpret the spatial distribution. So, this section begins with presenting some statistical techniques that can show the distribution of elementary schools with respect to population and districts. This is followed by using some GIS spatial analysis functions that can assist in identifying the center of schools, the distribution pattern of schools, directional trends, the relationship between schools and other land uses, the clusters of the schools, and, finally, the suitability of current school locations and suitable locations for future schools.

Spatial distribution and density of elementary schools
The analysis of elementary school distribution has been conducted in both statistical and spatial scales within Najran districts. As shown in Figure  2) and Table 1, Najran city had fifty-three elementary schools in 2019, and those schools were distributed among thirty-nine out of seventy-eight districts. This means only 50% of the districts had elementary schools. It can also be noticed from Figure 2) and Table 1 that two districts have four schools for each district (Alfahad and Alghwela), Dahdha district has three schools, six districts have two schools each, and thirty districts have one school each. Thirty-nine districts do not have schools; only two of them are unpopulated.
The density of schools helps to identify districts with a more significant or lower number of schools than the others; this can be counted based on the area or the population size. Measuring school distribution per district area may not give a comprehensive idea of the school distribution in residential districts, so looking at the relationship between the number of schools and the population of each district is a better way (Alsagri and Aldagheiri 2013), since the population is the main factor in the educational process. The Pearson correlation result is (0.68), which means a positive correlation between school numbers and the population size in each district. Many previous studies found a positive relationship between the number of schools in the district and the population size (Alsagri and Aldagheiri 2013; Alsalem 2011; Dawod et al. 2013). This study considers an elementary schools' average per 3,600 people in districts, since this is the standard issued by MOMRA and Riyadh Municipality. In Najran, as shown in Table 2, with the exception of districts not  having schools -which represent half of the city's districts -the study finds 20.5% of districts have schools but less than the standard (1:3,600) meaning, for each school, the average of population ranges from 3957 to 19,233 persons. Most of those districts can be considered as old districts that have been fully developed and have a higher population density; however, 28.2% of the districts have more schools than the standard, which means that the average population per school ranges between 247 to 3,373 persons, and most of those districts are located on the fringes of the city; they are villages in the southern, western, and northern parts or new districts with a low population size. The study found that elementary schools' average per population in Najran is 1:5,970 people; however, there are thirty-nine districts without schools, where most of them are new districts that have started growing and need schools urgently. Population size in some of them began to increase sharply, so some of them require more than one elementary school. Students living in districts without schools join schools in neighboring districts. They suffer when commuting to and from schools, especially with the lack of school buses and public transportation.
To be more specific, Location Quotient (LQ) shows the extent of spatial concentration or inequity of elementary schools in the districts regarding the number of populations. If the LQ value is less than 1.0, the local concentration of elementary schools is less than expected given the trends in the city as a whole; if your LQ value is 1.0, then the local concentration of elementary schools is as expected given the trends in the city as a whole; and if your LQ value is greater than 1.0, then the local concentration of elementary schools is more than expected given the trends in the city as a whole. As shown in Table 1, the LQ of twenty-nine (55%) districts varies between 1.03 to 24.17, meaning that those districts have a higher concentration of elementary schools than the whole city, and it can be higher if districts have a lower number of populations per school. Most of these districts are distributed in all parts of the city. However, the LQ of nine (17%) districts varies between 0.31 to 0.95, which means that those nine districts have a lower concentration of elementary schools than Najran city; this can be noticed in districts that have a higher number of populations per school, and most of those districts are the old and fully developed districts that do not have enough schools. In this Lorenz  Curve, and as shown in Figure 3, 50% of elementary schools are enjoyed by around 50% of the population, but 100% of the schools are only enjoyed by 78% of the population. This shows that the city lacks elementary schools in some districts, resulting in more pressure on some of the available schools. This outcome is supported by previous studies which found that in many Saudi Arabian cities, districts in proximity to the city center have a greater number of schools than what is located further away due to the higher number of populations within those schools, and some of the districts located in the city fringes had a shortage in schools (Alharbi 2018;Alqahtani 2018;Alrehili 2015;Belarem et al. 2018;Murad, Dalhat, and Naji 2020;Zabedi 2010). Based on the above results, the author's hypotheses that each elementary school covers 3,600 persons, and each district has at least one elementary school, can be rejected.

Methods of measuring geographic distributions
These methods measure the spatial concentration, direction, dispersion, and spread of elementary schools and include the tool of mean center, central feature, standard distance, and directional distribution. Using GIS tools revealed that the mean center is close to central feature with a slight deviation of 2.7 km towards the west, which means a higher number of schools in the city center and western districts (Figure 4). Standard distance is an important GIS tool that can measure the  degree to which school locations are concentrated or dispersed around their center (Esri 2020a). As shown in Figure 4, the standard circle radius is 13,608 meters, and the circle is located in the central parts of the city; it includes 37 out of 53 schools, representing 69.8% of the total number of schools. This indicates that elementary schools are concentrated in the residential districts near the city center, and there are fewer schools towards the peripheries. The standard area covered 202 km 2 , representing 52% of residential districts' total area (386 km 2 ). This can be an indicator that schools are clustered in densely populated residential districts and vital areas in Najran, but most of those schools are distributed randomly. Those observations align with many of the previous studies done in Saudi Arabia, since most of them found that schools are clustered in highly populated districts and they are distributed in a random way (Alhajri 2016;Alsagri and Aldagheiri 2013;Alharbi 2018;Alquraini 2001;Al-Zeer 2005). Directional distribution (Standard Deviational Ellipse) is another significant function that can summarize the spatial characteristics of geographic features including central tendency, dispersion, and directional trends (Esri 2020a). As shown in Figure  4, the directional trend distribution shows that the standard distance is in the X-axis direction is 18.6 km, Y-axis is 4.7 km, and the distribution's deflection value is 71.6°. This means that the distribution of schools in Najran takes a direction trend from southwest to northeast, and this could be due to the city's linear shape within a flat land surrounded by rugged mountains in the north, south, and west.

Density analysis
This method helps determine the locations of elementary school concentrations in Najran and their relevance to surrounding land uses or roads. Point density produces a surface map that shows the distribution density extent of elementary schools within the area (Dawod 2012). Figure 5) shows that the highest density is in two areas in the city: the first is the old, highly populated and developed districts, and the second one is located in both previous areas, C.B.D districts, and some areas in the southern part of the city that can be considered a village, where residents could convince the officials to establish new schools. The lowest density is noticed in most parts of the city, especially towards the eastern part.
Kernel density is one of the GIS functions that shows a circular neighborhood link that reflects the elementary school density in each circle, and surface trends are determined based on the geographical spread of schools, so it is concentrated in areas with high school density while it recedes in low-density areas. Figure 5) shows that schools' higher density is in old and fully developed residential districts and the residential districts near the city center. Then, it declines moving east towards the fringes; it shows similarity with point density results. Most of the previous studies showed that a greater density of schools was found in proximity to the city centers where the districts were full of residents.

Analyzing patterns
Knowing the patterns of elementary schools leads to a search for the factors affecting its formation or determining if the distribution is random. Some GIS techniques help to find the spatial distribution type of elementary schools in Najran. Nearest neighbor analysis is an important and accurate quantitative technique that attempts to determine the distribution patterns of a phenomenon spatially and whether the distribution is clustered, random, or dispersed. As shown in Figure  6, the nearest neighbor ratio is 0.85, which means the distribution pattern of elementary schools is clustered, but it tends towards the random pattern, and there is a less than 5% likelihood that this clustered pattern could be the result of random chance. Also, this means that some schools are concentrated in small areas with a short distance between each other. The rest of the schools are spread over large areas and are far apart from each other. This can support what has been mentioned in the density section and previous studies that schools are concentrated in old residential districts, the number of schools is not enough in some districts, and, in some, there are no schools.
Ripley's K function is another important GIS technique that determines whether elementary schools' distribution patterns exhibit clustering or dispersion over a range of distances. Figure 6 shows that the observed K value is greater than the expected K value by around 12,800 meters; then, the observed K value becomes smaller than the expected K value for a short distance. This shows that the distribution of elementary schools is more clustered in most parts of the city, which can be consistent with the nearest neighbor analysis finding. This can be due to a higher number of schools in specific locations at an extremely high confidence level since the observed K value is larger than the upper confidence envelope value. These findings are consistent with many previous studies that found the distance between schools located in the city centers and students' homes are shorter than the distance from schools located in districts far from city centers to students' homes.
In addition, Moran Index is +0.26, as shown in Figure  6, which means that the distribution pattern of elementary schools in Najran is clustered. This agrees with the previous results, which show that most elementary schools are clustered mainly in old and highly populated districts. However, the main hypothesis of this study that assumed all boys' elementary schools are distributed equally within the city districts can be rejected.

Proximity
Proximity determines the extent of the phenomenon's proximity to similar or different geographic variables. Table 3. shows the comparison of professional authorities' standards, mentioned in the literature section, and the current situation of Najran elementary schools regarding the coverage and distances to other elements or land uses. The section below shows some types of proximity analyses, such as the buffer zone, proximity to other elements or land uses, and Thiessen polygons.
Based on GDMS, MOMRA, and Riyadh Municipality standards, elementary schools' buffer zones should be 500 m. It means that this is the maximum walking distance for students. As shown in Figure 7, twelve elementary schools' buffer zones overlay with each other. This is mainly found in old, highly populated districts and some southwestern villages. Also, the buffer of some schools almost intersected with other nearby buffers, which is noticed around six schools in the city. As we go towards the eastern side of the city, the distances increased between schools, meaning that many parts of the city are not served by schools; specifically, half of the city districts do not have elementary schools. The minimum distance between elementary schools is 402 m, while the maximum distance is around 7 km, and the average distance is 1.85 km, and most of the city sections lack safe sidewalks. This can be a significant indicator of the randomness of school location selection, reflecting the inequality of school distribution among the populated residential districts in the city. As stated in some of the previous literature, it is more common in some Saudi cities that buffer zones of schools located in city centers overlapped between many schools, while other far districts had a shortage of schools (Alharbi 2018;Belarem et al. 2018;Zabedi 2010). There is only one airport in Najran; it is on the city's eastern side and surrounded by new residential districts. Based on CDE, EPA, and GDMS standards, the distance between the airport and schools should be more than 3 km. In Najran, two schools were located within the specified distance from the airport. Gas stations are distributed throughout Najran, and based on EPA and GDMS standards, schools should be 300 m and 75 m, respectively, away from gas stations. In Najran, only one elementary school was located within 75 m of a gas station, but eighteen schools are located within 300 m of gas stations. Regarding power plants, based on GDMS, the distance between a school and power plants should be more than 500 m. Only two schools are found in proximity to power plants. This can be due to the local authorities' interest in selecting school locations as far away from gas stations and power plants as possible. Even if this distance to gas station can be considered a short distance, there is a need to increase it to 300 m as in the EPA standards since gas stations are considered a major source of danger. However, twenty-three schools are within 1 km from cooking gas cylinder distributors, as shown in Figure 8). This poses a significant danger to school buildings as these distribution sites are perilous.
Despite the importance of main roads and their significant role in facilitating access to services, they represent a great danger to students when schools are in their vicinity. Accordingly, specialists have set standards related to the distance between elementary schools and main roads with the surrounding areas; the distance ranges between 150 m to 800 m, as mentioned in the literature section. Figure 8) shows that fourteen schools are located immediately next to highways, and fourteen schools are next to main roads. This means that 53% of elementary schools were placed in proximity to dangerous roads. Also, forty-seven schools are located within 450 m of main roads or highways in the study area. This shows that many students are in danger either in the morning or when they leave schools. Also, those roads produce air and noise pollution, which affect students' health and achievements negatively. As found in previous studies, it is common in Saudi Arabia to choose elementary schools in proximity to roads to increase the accessibility to schools' locations (Pasha 2004;Zabedi 2010), but those locations have elevated air pollution and noise, which affect the schools' populations negatively.
Factories usually emit dangerous gases and discharge chemicals into the air, water, and ground, which causes serious health problems for surrounding communities. Industrial machinery and processes produce noise, which disturbs students' attention. The UNESCO, EPA, and GDMS set a distance of more than 200 m, 300 m, and 150 m, respectively, from the closest schools. In Najran, as shown in Figure 9), seven schools are located within a distance of less than 200 m, and thirteen schools    are less than 300 m from industry activities (e.g., car maintenance, blacksmithing, factories, iron factories, wood factories). Floods are considered natural hazards and disastrous, leading to the destruction of both environmental elements and human lives. GDMS sets 300 m and EPA sets 400 m as a minimum distance between valleys or streams of torrents to schools. However, in Najran, nineteen elementary schools are located less than 300 m from Najran valley or torrent streams, as shown in Figure 9). This is because Najran is located on the edges of a big valley, and many torrent streams run through the urban area. Not many studies have been found in the literature investigating the proximity to some dangerous or noisy land uses. These findings can reject this study's assumption that school locations follow the standards of school site selection.
Thiessen polygons show the catchment area of each current school. The minimum Thiessen area is 1.2 km 2 , the maximum is 350.3 km 2 , and the average is 39.4 km 2 (see Figure 10). The small catchment areas that are less than 8 km 2 are located in old and fully developed districts and close to the city center. They are surrounded by catchment areas ranging between 8 to 35 km 2 . However, catchment areas more than 60 km 2 are noticed in new districts, which are in the city fringes and eastern plains. In these, the catchment areas are different and heterogeneous in their size in the city. This is due to school clusters in the old districts and districts near the city center and few schools in the fringes. So, it is suggested that large catchment areas need new schools since the number of residents are growing dramatically, and students suffer from commuting long distances to reach schools.

Spatial interpolation
Inverse Distance Weighted (IDW) and Kriging were used. IDW are valuable tools that can estimate values based on the average values of the surroundings cells (Esri 2020b). As shown in Figure 11), the highest concentration of schools is shown in the northern part of the old and fully developed districts, where the higher population density is, and it can also be noticed in Alghwela district. This represents about 20% of the city area. However, the lower density could be observed in villages in the south and west of the city, east of old districts, and in some parts of Alghwela and Almarkab districts, representing about 35% of the city area. Towards the city's eastern side, the school density decreases gradually until reaching Najran University, where it is the lowest density. Kriging generates an estimated surface from a scattered set of points with z-values (Esri 2020b). These geostatistical procedure results are almost like the results of (IDW), where the schools' density is mainly higher in mid-northern districts, which are fully developed and have a higher population density. The density becomes lower upon reaching the eastern or western side of the city (see Figure 11) (. These results prove that schools are clustered in certain districts and dispersed in others within Najran city.

Hotspot analysis
Applying hotspot analysis identifies hot and cold spots of elementary schools in Najran. The results reinforce previous results, indicating that hot spots are clustered in mid-northern parts of the city where the old and fully developed residential districts are (see Figure 12). However, the cold spot spread across the new and less densely populated residential districts that are mainly located in the eastern part of the city; also, there are some cold spots that can be noticed (90% confidence) in the neighborhoods surrounding the city center and villages located in western and southwestern parts of the city.

Current status of public elementary schools according to degrees of suitability
The current status of elementary school locations in Najran is not similar in all districts due to different natural and human characteristics of areas surrounding schools; some districts are very old, highly populated, surrounded by mountains, or penetrated by highways, main roads, or valleys. Therefore, it is sometimes difficult to achieve suitability for service locations, but planners should do their best. The author investigated the current school sites in terms of adherence to the standards mentioned above of CDE, EPA, and GDMS, since those standards cover many factors. Based on data availability, nine factors are used to determine the suitability degree of schools' locations. The highest weight is given to variables related to students' safety, such as proximity to roads, valley, and power plants, followed by proximity to factories, gas stations, gas cylinder distributors, the airport, the neighborhood center, and the closest school. As shown in Table 4, no school is found in  very suitable or suitable locations, which means no school in Najran follows the nine factors; fourteen schools are in good locations since three factors are not applied to the school's sites. Twenty-eight schools are in fair sites with lower suitability than the previous ones since four or five factors are not applicable. Eleven schools are in unsuitable locations since they do not apply most factors. These results call for pessimism about the suitability of current school locations in Najran, as many schools are in proximity to some sources of danger or nuisance, while other districts are without elementary schools.

Suitable locations for boys' elementary schools in Najran city
Searching for suitable sites for boys' elementary schools in Najran has emerged as a priority in light of what has been observed regarding the current situation of school sites and the urgent need by some residents to have schools within their residential district. The GIS system has the advantage of finding the best suitable sites for any service. Therefore, the researcher uses this system to build a suitability model that suggests suitable locations for boys' elementary schools in Najran. Twelve criteria are considered to develop a map showing suitable and unsuitable locations for schools. Those criteria include population density, proximity to closest elementary schools, the neighborhood center, the closest highways or main roads, the airport, gas stations, gas cylinder distributors, factories, power plants, and valley or streams. Although the author intended to include more variables, some data is not available. Due to applying many factors, Figure 13 demonstrates the scarcity of entirely suitable sites; the tendency toward fair and good locations and suitable locations are on the city's eastern side. However, it is still possible to find some suitable locations for elementary schools in the western, northern, and middle parts of the city that comply with most of the criteria. By applying the MOMRA and Riyadh Municipality standards that state, "there should be a boys' elementary school for each 3,600 population", Najran city is in need of thirty-five new elementary schools; this is only based on the population of each district. However, considering the longest walking distance to school and that each neighborhood should have an elementary school, this will require establishing around 130 schools.

Conclusions and recommendations
Elementary schools provide one of the basic educational stages; it is the main nucleus of future studies. Therefore, studying current educational service spatial distribution and suggesting future locations is very important for educational agencies. In Najran city, it has been noticed that, to some extent, there is a positive correlation between school numbers and the population density. Also, elementary schools follow a clustered distribution pattern in that they are concentrated in old and fully developed districts that are mainly located in proximity to the city center; the buffer zones of twelve schools overlapped with other schools, but their distribution tends toward the random pattern. On the other hand, students in half of the city districts took a long time to reach their schools since their districts are not covered by elementary schools, despite most of those districts developing quickly and urgently needing schools. This situation is also noticed in many cities in Saudi Arabia, as shown in the literature review section.
Regarding the distances between boys' elementary schools and impactful land uses, only very few schools are located within the specified distance from the airport, power plants, and gas stations. However, 53% of boys' elementary schools in Najran are located near highways, 25% are located in proximity to factories, and 36% of the schools are located along the edge of the valley. Investigating the suitability of elementary schools' current locations shows that no school is found in a very suitable location, while around 53% of schools are located in fair locations that follow a few of the standards, and 21% of the schools did not follow almost all of the school site selection standards.
Thus, local educations agencies and planners must evaluate current school locations to find whether they constitute an actual or potential endangerment of school users' health and safety, or corrective measures should be taken that will result in danger and noise mitigation to levels that will not constitute endangerment. Also, it is recommended that they build barriers (e.g., berms or walls) between schools and highways to reduce air pollution and noise levels and to protect students. Also, it is suggested that educational agencies need to clearly define and update the current standards, combine all of them under one major guideline, and take advantage of international professional standards for selecting elementary schools' locations. Then, they should establish new schools to fill the deficit in fully developed and far-located districts, especially as the population is increasing sharply during this period. In most cities, many districts still have suitable locations for new elementary schools, and many districts have vacant lands designated for schools that are already in suitable locations. Future research can use the updated standards to investigate the current spatial distribution of schools and the demand for new schools in the future. Also, future research can add additional factors when investigating current schools' locations or suggesting locations for future schools. Finally, future research can compare the spatial distribution of boys' and girls' schools, when the data becomes available.