Spatial Analysis of Urban Hierarchy Based on the Formation of Urban Stair System in Iran

Introduction
Cities accept different roles and functions based on their characteristics with different power and influences. More attention is paid to some cities. This leads to reduction of the importance of other cities and finally, this leads to development of urban primacy phenomenon. Urban hierarchy as one of important subjects in urban studies includes several topics such as stair system of urban hierarchy. Along with development of urban primacy in this system, a kind of internal order is developed among the cities and a hierarchical system is created. These groups are formed via population gap on a linear curve. This urban hierarchy system is faced with some questions on the relationship between spatial pattern of urban groups, pervasiveness of the stair system, the number of cities, the number of urban population, the urban primacy coefficient and the number of urban groups. This paper investigates these issues in Iranian urban hierarchical system.
 Methodology
The present article is conducted via descriptive analytical method with documentary and library studies. In order to answer the research questions, first of all the status of the cities in urban hierarchy was examined using rank-size model and then the stair system in national and regional scale. In the next phase, spatial dispersion of the cities was displayed using the GIS to investigate the relationship among the cities in a group and their spatial dispersal. Census studies were also carried out by Iran's Statistical Center in 2010. Finally, the aim of this research is based on spatial distribution analysis of cities in stair system of urban hierarchy, the average of nearest neighborhood, multi-distance spatial cluster analysis and standard deviational ellipse methods. At the end of the research, Spearman test was used to understand the relationship between the numbers of urban population with the number of groups in the stair system. The statistical population of the present study is all the cities of the country at national and regional scale. Out of 30 provinces, 10 provinces were studied as the research sample.
Results and discussion
Findings showed that different regions of Iran are very different in terms of the number of cities and population. Among them, Khorasan Razavi province has the greatest number of cities (72 cities) and Yazd Province has the lowest number of cities. In terms of population, the urban population in different regions has fluctuated from 800 thousands to more than 11 million people; as Tehran and Khorasan Razavi have had the highest number of population and Hormozgan and Yazd have had the lowest number of population in the sample. On the other hand, based on the studies, West Azerbaijan with 9 groups and Chaharmahal-o-bakhtyari with 5 groups, have been ranked as the first and the last of urban groups in regional scale, respectively.  It is interesting that the lowest number of urban groups is seen in the national scale. Based on the above mentioned cases, urban system in Iran at both national and regional level is faced with stair system of urban hierarchy. This characteristic comes from the urban primacy. On the other hand, the group-mate cities in this system, not only are not in the same area, but also they are dispersed in the region without any specified pattern. Group-mate cities don’t create isochromatic zones in the region based on urban groups' dispersion map. Accordingly, it is not possible to determine a border for group-mate cities. Therefore, cities contrary to the stair system on the diagram don’t follow any order geographically. There are significant differences in this field between urban groups. Most important of them are stair system is not visible in low population urban groups in some regions (Yazd and Mazandaran). In some regions urban groups have very low members (2-3 members), some regions in terms of the number of groups and city frequency are in balance and the provincial capitals are the most regular. Results show that there is no relation between dependent variables including number of cities, number of urban population, urban primacy coefficient) and independent variables, number of urban groups. This means that the increase or decrease in the dependent variables have no effect on the number of city groups as independent variable.
Conclusion 
Investigation about urban network of Iran in both national and regional level shows that there is no harmony with rank-size model in urban hierarchy. This indicates undesired relations between cities. Thus, urban primacy is a dominated phenomenon in Iranian urban system. However, this phenomenon appears in different patterns named as stair hierarchy. Study of urban system in Iran confirms the existence of stair system in urban hierarchy at both national and regional levels. This system divides the urban hierarchy into several urban groups. The group-mate cities are separated from upper and lower level cities due to the population gap. It seems that they make a new form of urban hierarchy. In this system, the cities could be classified into several groups and each of them developed more homogenous hierarchy system compared with the whole urban system in the region. One of the most important issues in this area is identification of the main factors, because the variables have been studied in this research are not the main factors in the development of the stair system. Study of this system and mechanism of its function can lead to the identification of new dimensions of urban hierarchy system at the other scales. This research can achieve better results, provided that it is done as a comparative study at different scales ranging from regional, trans-regional and international scales.