This study used a case study approach to achieve the research objectives, in which the city research method was used to obtain data for the study and the quantitative analysis method was used to determine the relationship between each indicator and urban grain. In the first phase (
Figure 1), urban grain’s spatial indicators were identified based on a literature review, which provided the basis for determining the content of the study. In the second stage (
Figure 1), the study areas included Jinan Shangbu (fine grain) and Tangye New District (coarse grain), and experimental data were acquired using open-source data in combination with urban research. In the third stage (
Figure 1), a data analysis was performed. Additionally, a visual graphical comparison of spatial indicators between the coarse- and fine-grained study areas were carried out, and finally, the relationship between urban grain and spatial indicators was analyzed to determine the spatial indicators of urban grain.
2.1. Spatial Indicator Extraction
The research objective of this study was to identify the spatial indicators that influence urban grain and to regulate these indicators to change urban grain and, thus, promote sustainable urban development. Therefore, it was necessary to screen and transform the factors into quantifiable and modifiable spatial indicators. A total of 32 papers related to urban grain indicators were screened in a literature review. Previous research has identified physical factors affecting urban grain, including streets and traffic, density, building age, and the natural environment. The literature on streets and traffic indicates that the division of streets affects the framework of a city and that shorter streets with higher intersection regularity can bring fine grain; road network density is the reason behind this phenomenon. It has been proposed that the average building facade width of streets in fine-grained areas is shorter, increasing the visual richness of the streets [
17,
20]. Therefore, building facade widths along streets represent a spatial indicator. In addition, the literature indicates that areas with low building density have greater spacing between buildings and are, therefore, less easily formed into a fine grain. The literature on building age points out that areas with old buildings are generally self-built, occupy smaller regions, and are more finely divided; thus, the age of housing structures serves as a regulating indicator for urban grain. The natural environment is mainly related to natural disasters and patterns, which are difficult to regulate and, therefore, are not considered a spatial indicator.
In addition, economic, social, and cultural factors were translated into quantifiable physical indicators. Among the literature on real estate development and industrial structure, the division of land parcels by function was proposed, and large-scale blocks with a single function led to the disappearance of fine grain. Therefore, a land-use mix describing the degree of mixing of land-use types and functional attributes within a given urban block [
47] was used to convert the index. In addition, the number of use units in large-scale parcels is low due to single industrial structures, which can be reflected in the spatial factors, as the number of external entrances and exits of buildings is reduced; thus, the economic factors were converted into numbers of entrances and exits of buildings along streets. The literature on policies indicates that policy formulation fundamentally impacts urban grain. Therefore, the physical factors that influence urban grain size (road network density, building density, etc.) can all be used as spatial indicators for their transformation. The literature on construction technology indicates that technological advances have made large-scale buildings possible, thus contributing to coarse grain generation. Additionally, the older the building, the more backward the construction technology, thus showing that construction technology is related to a building’s age, translating it into an indicator for the age of a housing structure. Similarly, the literature on history and culture indicates that the legacy of history and culture creates a particular preference for building scale and road network density. The literature on heritage conservation suggests a preference for preserving old buildings with historical value, which are usually small in scale due to technical constraints; thus, cultural elements could be translated into building density, road network density, and the age of housing structures.
In summary, the spatial indicators were identified as road network density, building density, age of housing structures, building facade width along streets, number of entrances along streets, and function mixture (
Table 1) based on relevant and related research, which is assumed to be correlated with urban grain and analyzed empirically.
2.2. Data Analysis Method
The Conzen School emphasizes the following two basic approaches for studying urban form: a synchronic analysis based on a geometric analysis, and a diachronic analysis based on historical maps [
48]. The synchronic analysis also emphasizes the analysis of the relative positions, contour scales, and arrangements of morphological elements within a city, which could then be grouped into different categories. The diachronic analysis emphasizes the comparative analysis of the process of change in the morphological elements in a city over time, which can then help determine the temporal relationship of the change in morphological growth. In this paper, a synchronic analysis was mainly utilized to compare two different grain-size areas over the same period to explore the spatial elements affecting grain size.
Norton argued that the research object of urban grain is the parcel [
8]; however, since urban grain’s spatial indicators contain multiple scales, such as building density, the width of a building facade along a street, and age structure, they are indicators at the level of building units. The number of entrances and exits are indicators at the block level, and the suitable research object will be selected according to the scale of the urban grain’s spatial indicators. Ding argued that urban fabric forms can be roughly divided into buildings, parcels, and blocks [
49], and urban grain is one of the elements that makes up urban fabric and can be analyzed using these three scales. Therefore, in this study, buildings, parcels, and blocks were selected as the research objects according to the scales of spatial indicators.
In this study, the grid system consists of analysis cells applied to integrate the relationship between people, land, function, transportation, and architecture. Previous research suggested that a grid scale of 50 m × 50 m in size could express the relationship of parcels in this study area; thus, this scale was chosen as the analysis cell of the study. Urban grain value was chosen as the dependent variable, which was used to observe how spatial indicators impact urban grain.
Firstly, the dependent variable of urban grain was analyzed. According to the definition of urban grain, the coarseness of urban grain was determined by calculating the number of intersection points of parcels in each grid [
8]. Consequently, the input vector data of the parcels in the study area were input into Arc GIS 10.2, after which the urban grain attributes of the parcels were connected to the grid by a spatial join, and the number of parcels in each grid was counted and visualized.
Subsequently, an analysis of the spatial indicators was performed. The first spatial indicator was building density. The building density indicator represents the kernel density of a building. The analysis consisted of importing a building’s base map of the study area in Arc GIS, extracting the building’s center points, and calculating their kernel density. Subsequently, the raster data of the kernel density to the center points of the 50 m × 50 m grid were extracted, and a spatial connection of the points to the grid was performed and visualized. In addition, the bandwidth (search radius) for calculating the kernel density was set to 100 m so that the values of building density could be homogeneously dispersed in each grid [
50].
The second spatial indicator was road network density. Similar to building density, road network density was compared by calculating the line density of the study area. The analysis procedure involved a line density analysis of road network data in Arc GIS (the bandwidth was set to 100 m), after which the raster data of line density to the center point of the created 50 m × 50 m grid were extracted and visualized.
The third spatial indicator was the age of housing structures, which was analyzed with the idea of using every ten years as a structural stratum. The number of levels spanned by the unit grid was assigned and visualized for comparison. The analysis involved importing the data in Arc GIS and assigning values according to the ages of the house structures, after which a spatial join between the 50 m × 50 m grid and the ages of the house structures was performed to obtain the number of house-age-graded structures in each grid and visualize them.
The fourth spatial indicator was the width of building facades along the streets. The main research object was the building facade width along the street in each parcel. The value of this indicator was calculated from the width of building facades along the streets in each grid. The analysis procedure involved importing the actual data on building facade width along the streets in Arc GIS (for buildings located at the corner of two roads, the sum of all street facades was entered). Subsequently, the 50 m × 50 m grid was spatially connected to the data for visualization.
The fifth indicator was the number of entrances along the streets. The value of this indicator was calculated using the kernel density of the number of entrances and exits along the block and visualizing it for comparison between the study areas. The analysis procedure involved importing the entrance data along the street area in Arc GIS, setting the bandwidth to 100 m, performing the kernel density calculation, and obtaining a kernel density raster map. Subsequently, the 50 m × 50 m grid center points were extracted, and the values of the raster map were extracted to the grid center points, spatially connected to the grid, and, finally, visualized.
The sixth spatial indicator was function mixture. The research object was to identify the parcel, link the data to the urban parcel attribute table of Arc GIS, make spatial links with the 50 m × 50 m grid to calculate the number of construction land categories in each grid, and visualize them.
In order to verify the relationship, Pearson’s correlation coefficient (Equation (1)) was applied in this study. Generally, Pearson’s correlation coefficient is calculated by dividing the covariance of two variables by the product of their respective standard deviations, and is usually denoted by
r. Pearson’s correlation coefficient is a measure of the linear correlation between two variables. The coefficient is widely used in the natural sciences to measure the correlation between two variables and reflects the strength of the linear correlation between them. If the r value is less than 0, it indicates that the two variables are negatively correlated. If the r value is greater than 0, it indicates that the two variables show a positive correlation, and the larger the absolute value, the stronger the correlation. When the
r value is equal to 1 or −1, it means that a linear equation can describe the two variables.
where
rp is the Pearson correlation coefficient;
x and
y are two variables; and
n is the number of samples.