Urban Expansion Assessment Based on Optimal Granularity in the Huaihe River Basin of China

Abstract

Determining the optimal granularity, which has often been ignored in the analysis of urban expansion and its landscape pattern, is the core problem in landscape ecology research. Here, we calculate the optimal granularities for differently sized cities in the Huaihe River Basin of China based on scale transformation and area loss evaluation. Accordingly, we construct a landscape index and urban land density function to analyze urban expansion and landscape pattern. The results can be summarized as follows. (1) Within the first scale domain of the landscape indices, the optimal granularities of Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou are 60 m, 50 m, 40 m, 40 m, and 40 m, respectively, which are the optimal units in the study of urban expansion. (2) The urban land density decreases from the urban center to the outskirts, the urban core of each city is more compact than the outskirts, and the land density curve parameter α of Zhengzhou is the largest at 4.693 and its urban core the most compact. (3) There are significant spatial and temporal differences in the urban land densities of differently sized cities. The urban land density functions of different cities are similar before 2000; after that, they are similar to the standard inverse S-shaped function and the land use density curve of large cities is closer to the standard inverse S-shaped function than that of small- and medium-sized cities. (4) Large cities have faster expansion, much larger land density curve parameter c than medium- and small-cities, stronger linkage development with surrounding areas, and a higher degree of urban centralization. Urban expansion compactness was influenced by urban locations and functions except for urban sizes. This study offers a method for identifying the optimal granularities for differently sized cities and also provides information for the decision-making efforts that concern the rapid urbanization in major grain-producing areas of China.

1. Introduction

Urbanization has entered into a rapid development period in the 21st century and urban expansion, as an important symbol in the process of urbanization, has become a hot topic of urban geography [1]. In the early discussion of urban expansion, there is often no associated definition and connotation, and it is objectively described as additional residential, industrial, and commercial urban land moving away from the city center [2], or defined as when two cities are close together and the rural space in between is embellished with new development [3]. Since the end of the last century, some scholars have defined urban expansion as an inefficient urban expansion process from the perspective of urban land use efficiency [4,5], and they formed a definition of urban expansion with a “pessimistic” color [6,7]. In recent years, a number of scholars have given a more neutral definition of urban expansion, arguing that urban construction land [8], changes in urban land and population size [9], built-up areas [10], impervious surfaces [11,12], etc., are the main contents of urban expansion. Thus, scholars mostly use remote sensing monitoring [1,6], GIS spatial analysis [13,14], fractal theory [15,16], landscape index measurement [17,18], cellular automata model [19,20], and other methods to study the phenomenon of urban expansion. From a macro perspective, they extract impervious surface area, monitor the change of urban construction land area, analyze urban land use efficiency, study the scale, space, and morphological characteristics of expansion, and predict the urban development pattern; from a micro perspective, they analyze the landscape pattern characteristics of urban expansion, and judge the mode of urban spatial expansion [21,22] (infill, expansion, enclave, and linear [23]), and thus provide a scientific basis for promoting green urbanization and sustainable development [24,25]. Gong et al. [26] used remote sensing monitoring to map the 1978–2017 global impervious surface dataset, which has been widely used in urban expansion research [27,28,29]. As an important factor in studying urban expansion [30], urban land density [31,32,33] is usually combined with gradient analysis, which reflects the radial pattern of cities [34]. Jiao et al., defined urban land density as the proportion of urban impervious surface and used an inverse S-shaped function to analyze the distribution law of urban land density in different countries [23,35,36] and verify the reliability of the method, which provides an important foundation for research on global urban expansion and its morphology.

Rapid urbanization, resulting in economic development and population growth, has triggered significant urban expansion [37,38], which has accelerated the degradation of natural landscapes and the loss of habitats and ecosystem services while reducing food supplies and biodiversity functions [39,40]. The interference of human activities has significantly impacted landscape patterns [41]. In order to describe changes in landscape patterns, researchers need to consider the appropriate analysis scale when constructing the landscape index [42]. Granularity refers to the characteristic length, area, or volume represented by the smallest identifiable unit in the landscape, and the granularity effect is the core issue of ecology [43,44]. In landscape pattern and ecological analysis, if the granularity is too small it is easy to cover up some important information with too much spatial information [45], and if the granularity is too large it will lead to “noise” being stronger than “signal”, thus causing misunderstanding of the variables [46]. Therefore, the optimal landscape granularity refers to the most suitable scale for landscape pattern analysis, which can reflect the ecological characteristics of the landscape. Since the landscape index is scale-dependent, there is an obvious scale effect or granularity effect in the changes between different scales [46]. Therefore, the suitable granularity range of the landscape can be analyzed according to the granularity effect. Combined with the information loss assessment method [47], information entropy [48] and other methods are used to determine the optimal landscape granularity. However, most studies have focused on urban landscape pattern changes based on urban expansion and landscape indices [17,49,50]; relatively few studies have addressed the issue of the optimal granularity for urban expansion. Moreover, in landscape pattern analysis, most studies use the resolution of remote sensing images as the optimal granularity without scaling, which may not fully reflect the landscape pattern characteristics, thus affecting the accuracy of the calculation [49,51]. Therefore, determining the optimal granularity has become a key issue that should be urgently addressed in the research on landscape patterns in urban expansion [52].

As an area that is sensitive to climate change, various ecological processes in the Huaihe River Basin are in a delicate balance and show strong vulnerability to external disturbances. The basin contains key development areas, ecological and agricultural restricted and prohibited development zones, and both highly urbanized and backward areas. Rapid industrialization and urbanization have changed the land use structure and caused problems such as fragmentation of the urban landscape and declining connectivity, which affects urban planning and the ability to improve the efficiency of land use, as well as the construction of ecological and resilient cities. Therefore, we select typical cities in the Huaihe River Basin as the target area from the urban landscape and urban land use levels and attempt to answer the following two questions. (1) What are the optimal granularities for urban landscape pattern analysis in differently sized cities in the Huaihe River Basin? (2) What are the spatial and temporal characteristics in the expansion forms of differently sized cities in the upper, middle, and lower reaches of the basin?

2. Materials and Methods

2.1. Study Area

The Huaihe River Basin is located in the east of China, between the Yangtze River and the Yellow River Basins, which is bounded between 111°55′ E~121°25′ E and 30°55′ N~36°20′ N. It belongs to the north–south climate transition zone, with the warm temperate monsoon climate zone to the north of the Huaihe River and the subtropical monsoon climate zone to the south of it. The river originates in the Tongbai and Funiu mountains and flows into the Yellow Sea, across five provinces (i.e., Henan, Shandong, Hubei, Anhui, and Jiangsu), and 40 cities, with a basin area of 270,000 km² (Figure 1). The fertile land in the basin is an important grain-producing area, and the output of wheat and grain accounts for about 50% and 20% of the national total output, respectively [53]. The total population of the Huaihe River Basin is 183 million, which accounts for about 13.31% of China’s total population. Its population density is 4.8 times the national average and it ranks first in the population density of China’s three major river basins (i.e., the Yangtze, Yellow, and Huaihe Rivers). In 2020, the Huaihe River Basin, with less than 3% of the total water resources of the country, supported about 13.6% of the population and 11% of the arable land, contributed 9% of the total GDP, and produced 1/6th of the country’s grain, thus the ecological environment withstands tremendous economic pressure [54]. The topography of the upper reaches of the Huaihe River Basin is mainly mountainous and hilly with a high altitude, and the cities in the region are generally small- and medium-sized. The middle and lower reaches of the Huaihe River Basin and the Yishusi River region are mainly plains with suitable climates and developed economies; accordingly, there are many large- and medium-sized cities in this region. In order to determine the optimal analysis granularity of urban landscapes, we select Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou as typical cities according to different watershed locations, urban scales, and urban functions (

Table 1. Introduction of five typical cities.

City	Size/Location	Function Description
Zhengzhou	Large city Middle reaches	An important city in central China and a national transportation hub.
Xuzhou	Large city Yishusi River region	Mining transformation and the central city in the Huaihai Economic Zone.
Yancheng	Large city Lower reaches	Eastern coastal city at the intersection of two national coastal development strategies and the Yangtze River Delta integration.
Xinyang	Medium-sized city Upper reaches	Located at the junction of Hubei, Henan, and Anhui provinces, Huaihe River’s main hub city.
Bozhou	Small city Middle reaches	The core development area of the Central Plains Urban Agglomeration with member cities of the Yangtze River Delta Urban Agglomeration.

) in the Huaihe River Basin to study the urban expansion forms and landscape patterns in 1990, 2000, 2010, and 2017 to provide valuable reference materials for policymakers in China to use in managing the rapid urbanization of major grain-producing areas of China.

2.2. Data Acquisition and Processing

The data in this study include urban impervious surface data, land use data, basic geographic information vector data, and socioeconomic statistics (

Table 2. Data sources.

Data Name	Data Specification	Scale	Data Source
The global land cover dataset with a resolution of 30 m from 1978 to 2017	The urban impervious surface data are obtained using a reliable impervious surface mapping algorithm and the Google Earth Engine platform.	30 m	Published by Gong et al., (2019) [26], Tsinghua University “40-Year (1978-2017) human settlement changes in China reflected by impervious surfaces from satellite remote sensing. Available online: http://data.ess.tsinghua.edu.cn (accessed on 3 December 2021)”
The 30 m annual land cover and its dynamics in China from 1990 to 2019	The land cover data are obtained by using the random forest classification method through spatiotemporal filtering and logical reasoning.	30 m	Published by Yang et al., (2021) [55], Wuhan University https://doi.org/10.5281/zenodo.4417810
Basic geographic information data	Vector data of provincial and municipal administrative boundaries, water systems, and road networks in the Huaihe River Basin.		National Basic Geographic Information Center “National Basic Geographic Information Database. Available online: http://www.ngcc.cn/ngcc/ (accessed on 3 December 2021)”
DEM	The spatial resolution of digital terrain elevation data is 30 m.	30 m	Geospatial Data Cloud “GDEMV3 30M DEM. Available online: http://www.gscloud.cn (accessed on 3 December 2021)”
Socioeconomic Statistics	Population and GDP in Socioeconomic Statistics		China City Statistical Yearbook “Available online: https://data.cnki.net (accessed on 3 December 2021)”

). The impervious surface data in urban areas come from the global land cover dataset with 30 m resolution for 1978–2017 [26] and the 30 m land cover dataset (1.0.0) in 1990–2019 in China [55]. The former is obtained using a reliable impervious surface mapping algorithm and the Google Earth Engine platform with an overall accuracy of more than 90%. The latter, used for auxiliary validation, was obtained using the random forest classification method and processed by spatiotemporal filtering and logical inference, with an overall accuracy of 79.31%. The vector data of provincial and municipal administrative boundaries, water systems, and road networks in the Huaihe River Basin come from the National Basic Geographic Information Center. The digital terrain elevation data come from the Geospatial Data Cloud website with a spatial resolution of 30 m. The GDP and population data come from the China City Statistical Yearbook.

The urban impervious surface data (from 1978 to 2017) with the original resolution of 30 m were resampled at 10 m intervals using the ArcGIS10.7 platform, and the impervious surface raster data of five typical cities in the Huaihe River Basin for the four periods of 1990, 2000, 2010, and 2017 were converted into a total of eight different granularity sizes of 30, 40, 50, 60, 70, 80, 90, and 100 m in raster files.

2.3. Selection of Landscape Indices

In order to reflect the landscape pattern characteristics comprehensively and with reference to previous research results [56,57,58], this study selected six landscape indices at the patch-type level that are sensitive to spatial granularity changes (

Table 3. Selected landscape indices at the patch-type levels.

Metric	Abbr.	Data Range	Unit
Class area	CA	CA > 0	ha
Largest patch index	LPI	0 < LPI <= 100	%
Perimeter-area fractal dimension	PAF-RAC	1 <= PAF-RAC <= 2	---
Mean patch size	MPS	MPS > 0	ha
Landscape shape index	LSI	LSI >= 1	---
Patch density	PD	PD > 0	1 #/100 ha
2 Number of patches	NP	NP >= 1	---
2 Mean contiguity index	CONTIG_MN	CONTIG_MN >= 0	%

¹ #—Number of patches. ² Number of patches (NP) and mean contiguity index (CONTIG_MN) are taken into account to analyze the landscape pattern at the optimal granularity.

), including the total class area (CA), largest patch index (LPI), perimeter-area fractal dimension (PAF-RAC), mean patch size (MPS), landscape shape index (LSI), and patch density (PD).The above landscape indices were calculated using Fragstats (v4.2.1) software (“Available on: http://www.umass.edu/landeco/research/fragstats/fragstats.html (accessed on 12 December 2021)”) and imported into Excel for normalization, and then plotted the granularity effects.

The normalized landscape indices show significant or nonsignificant scale turning points with changes in spatial granularity [59], also known as inflection points. The area between the inflection points is the granularity domain, within which the landscape index changes relatively smoothly and can well reflect the characteristics of the regional landscape pattern. The scale domain defined by the first inflection point in the landscape index changes with spatial granularity can be used as a reasonable range in landscape pattern analysis [60].

2.4. Calculation of the Optimal Granularity

The transformation of spatial scale inevitably leads to different degrees of information loss, and area information conservation evaluation is an effective method to quantitatively discern the accuracy of raster granularity change [61]. This study combined granularity effect plots and the area loss evaluation method [61] to determine the optimal granularity for urban landscape pattern analysis. The formula of the area loss evaluation method is as follows:

$$E=A_{\mathrm{g}}-A_{\mathrm{b}},$$

(1)

$$L=E/A_b*100,$$

(2)

where E represents the absolute value of the landscape area loss, A_g represents the area after landscape type scale conversion, A_b represents the reference area (at 30 m resolution) before landscape type scale conversion, and L represents loss of accuracy in landscape type (%).

2.5. Gradient Analysis

We divided each city into a series of 1 km concentric rings using the central business district (CBD) and the geometric center of the impervious surface as the center of the ring, and selected an edge ring, which is able to accommodate a continuous functional urban area and excludes small cities far from the urban core, as the city boundary [35]. Taking the CBD in 1990 as the center, we created 1 km buffers in an increasing, stepwise manner (Figure 2). Each city was partitioned into a series of 1 km rings extending outward from the center.

2.6. Urban Land Density Function

By calculating the urban land density of each ring in the buffer zone, we can determine that the rate of urban land density, which decreases from the center to the outer rings according to a modified inverse S-shaped function, characterizes the spatial distribution of the urban land density within a city. Jiao [35,36] uses a modified four-parameter sigmoid function to fit the urban land density function points of the study regions. The basis of the method is to fit a nonlinear function to the observed data by refining the parameters in successive iterations. The Trust-region algorithm is used in this study. We fit the urban land density functions with MATLAB R2018a. The density from the city center for five different sized cities has been modelled using Equation (3).

$$\mathrm{f}(r)=\frac{1-c}{1+e^{\alpha ((\frac{2r}{D})-1)}}+c$$

(3)

where f(r) represents the urban land density; r represents the distance from the city center; e is Euler’s number; and α, c, and D are the estimated parameters of the model.

Parameter α controls the slope of the urban density function curve, which can be used to reflect the macro pattern of the urban form, and the higher the value of α, the more compact the urban form. Parameter c denotes the urban land density near the city boundary and D represents the estimate of the radius of the urban area, both of which will increase with urban expansion [35].

3. Results and Analysis

3.1. Calculation of the First Scale Domain and the Optimal Granularities of Differently Sized Cities

In order to identify the inflection points in the landscape index changes in decades with spatial granularity, the means of six landscape indices in Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou were calculated (Figure 3). The three landscape indices of the total class area (CA), largest patch index (LPI), and perimeter-area fractal dimension (PAF-RAC) show obvious inflection points or irregular characteristics. Among them, the CA index of Zhengzhou presents irregular characteristics with the change of granularity, and the corresponding CA indices of Xuzhou, Yancheng, Xinyang, and Bozhou all show two obvious inflection points, which are 50/70 m, 60/90 m, 60/80 m, and 50/80 m, respectively. There is no regularity in the LPI index of Yancheng, Bozhou has three inflection points (40/60/90 m), and the other cities have two obvious inflection points. With the increase of granularity, the PAF-RAC indices of the five cities show a general trend of rising rapidly at first and then rising slowly, with two obvious inflection points, whereas the inflection points corresponding to the mean patch size (MPS), landscape shape index (LSI), and patch density (PD) are not obvious or show no inflection points. Two of them, the LSI and MPS indices, show a downward and an upward trend as a whole, respectively, with the change of granularity, presenting an insignificant inflection point, but concentrated at 60 m. The PD index shows an overall decreasing trend, and Xuzhou has an unobvious inflection point at 60 m, while other cities have no inflection point. The PAF-RAC and MPS indices show an increasing trend, and the degree of disturbance caused by human activity on the landscape pattern increases. The LSI and PD indices continue to decrease, and the fragmentation of the landscape gradually decreases. By contrast, the CA and LPI indices change irregularly, which indirectly reflects the uncertainty in disturbances caused by human activity.

The variations in the annual average landscape indices with granularity are shown in Figure 3, and the first scale domain of typical cities in the Huaihe River Basin is shown in

Table 4. The first scale domain of the landscape indices (unit: m).

City	CA	LPI	PAF–RAC	MPS	LSI	PD
Zhengzhou	Irregular	30~40	30~60	30~60	30~60	No inflection points
Xuzhou	30~50	30~50	30~60	30~60	30~60	30~60
Yancheng	30~60	Irregular	30~40	30~60	30~60	No inflection points
Xinyang	30~60	30~50	30~40	30~60	30~60	No inflection points
Bozhou	30~50	30~40	30~60	30~60	30~60	No inflection points

. It can be seen that the first scale domains of the landscape indices with inflection points are significantly different, the first scale domains of CA are mostly 30~50 m and 30~60 m, LPI are 30~40 m and 30~50 m, PAF-RAC are 30~40 m and 30~60 m, while the first scale domains of MPS, LSI, and PD are all 30~60 m. Therefore, the inflection points corresponding to the first scale domains of Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou mainly appear at 40 m, 50 m, and 60 m. The area loss evaluation method (Figure 4) is used to calculate the landscape area loss for three different granularities, and when the landscape granularity is 60 m, Zhengzhou has the least land area loss from 1990 to 2017, which is only 0.110, so 60 m is the optimal granularity to use in the analysis of Zhengzhou’s landscape pattern. It can also be seen that the optimal granularity in Xuzhou is 50 m, and those in Yancheng, Xinyang, and Bozhou are all 40 m.

3.2. Variations in the Landscape Indices under Optimal Granularity

Based on the optimal granularity in Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou, landscape indices such as the patch number, mean contiguity index (CONTIG_MN), and mean patch size were used to analyze the urban landscape characteristics of concentric rings (see

Table A1. Landscape indices of five major cities under optimal granularity.

Zhengzhou	1990			2000			2010			2017
Ring	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS
1	1	0.945	309.24	1	0.946	309.6	1	0.949	311.04	1	0.95	312.84
2	1	0.914	876.96	1	0.924	889.56	1	0.926	893.52	2	0.465	450.72
3	1	0.936	1518.84	1	0.948	1549.8	1	0.949	1553.04	1	0.952	1559.88
4	8	0.295	248.265	5	0.254	421.704	2	0.472	1079.46	2	0.474	1086.48
5	15	0.123	160.344	6	0.195	433.26	1	0.939	2744.64	1	0.945	2779.56
6	73	0.172	29.574	33	0.153	81.829	14	0.217	220.834	8	0.231	409.77
7	186	0.22	9.426	99	0.173	25.96	39	0.2	85.366	12	0.096	306.3
8	276	0.195	4.882	186	0.195	11.563	56	0.18	61.014	16	0.19	253.598
9	294	0.204	4.61	204	0.236	9.522	87	0.233	39.914	44	0.235	99.245
10	329	0.187	3.435	267	0.202	6.395	148	0.199	23.891	40	0.218	119.304
11	429	0.17	2.455	366	0.183	4.343	178	0.177	21.212	47	0.177	114.74
12	457	0.164	2.325	420	0.175	3.455	249	0.184	13.888	72	0.189	73.73
13	385	0.172	2.826	408	0.191	3.425	290	0.233	11.035	132	0.174	40.751
14	492	0.156	2.15	500	0.169	2.681	330	0.206	9.329	142	0.188	40.178
15	490	0.147	2.172	485	0.164	2.705	414	0.178	6.232	260	0.167	20.161
16	483	0.143	1.921	489	0.162	2.244	483	0.189	4.562	283	0.207	18.24
17	573	0.139	1.696	580	0.151	1.983	559	0.178	3.579	370	0.211	12.407
18	585	0.131	1.737	568	0.138	2.17	521	0.165	3.893	422	0.196	10.699
19	594	0.136	1.472	587	0.156	1.808	592	0.178	3.174	491	0.234	9.003
20	585	0.141	1.596	585	0.146	1.825	558	0.17	3.288	512	0.197	8.285
Xuzhou	1990			2000			2010			2017
Ring	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS
1	1	0.949	301.25	2	0.558	150.875	1	0.948	302	1	0.949	300.25
2	5	0.251	169.3	4	0.317	216.438	5	0.22	174.05	1	0.936	883
3	30	0.181	36.35	25	0.229	47.36	6	0.399	215.958	5	0.394	264.45
4	71	0.269	13.718	58	0.244	21.608	32	0.26	45.461	15	0.309	102.283
5	103	0.244	9.007	80	0.225	15.719	36	0.212	48.271	24	0.31	80.927
6	155	0.278	6.147	145	0.268	9.093	83	0.238	24.307	49	0.243	49.199
7	171	0.264	5.104	159	0.276	7.978	109	0.228	19.083	62	0.206	43.589
8	167	0.273	4.418	153	0.28	6.842	151	0.252	13.886	84	0.219	36.991
9	227	0.24	3.371	207	0.258	4.866	162	0.272	12.694	124	0.268	24.127
10	235	0.245	3.211	223	0.26	4.436	212	0.226	9.075	170	0.244	16.649
11	242	0.251	3.217	272	0.246	3.41	278	0.268	5.973	240	0.249	11.943
12	235	0.255	2.934	229	0.28	3.778	302	0.245	5.217	247	0.252	11.867
13	217	0.245	3.431	221	0.266	4.337	267	0.262	6.155	324	0.239	8.378
14	233	0.253	2.643	251	0.281	3.27	310	0.269	3.838	422	0.246	5.242
15	194	0.25	2.999	212	0.246	3.406	251	0.259	4.284	343	0.221	5.754
16	192	0.258	3.322	181	0.314	4.435	216	0.297	4.753	358	0.253	5.026
17	179	0.25	2.856	199	0.225	3.206	224	0.258	3.732	327	0.255	4.657
Yancheng	1990			2000			2010			2017
Ring	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS
1	12	0.138	19.347	4	0.23	72.32	3	0.313	98.88	2	0.473	151.12
2	49	0.183	9.838	11	0.222	69.251	4	0.306	210.92	4	0.331	216.52
3	130	0.175	2.03	80	0.179	9.13	25	0.158	45.504	15	0.229	87.541
4	86	0.168	0.919	177	0.179	1.577	144	0.221	6.089	57	0.214	24.104
5	75	0.169	1.052	188	0.172	1.439	173	0.203	5.004	111	0.263	13.493
6	67	0.098	0.7	155	0.152	1.052	161	0.219	5.212	200	0.214	8.314
7	35	0.119	0.526	74	0.121	0.664	166	0.219	3.954	273	0.193	5.873
8	33	0.158	0.64	66	0.128	0.693	177	0.218	3.81	263	0.206	5.783
9	48	0.186	0.807	73	0.18	0.877	243	0.221	2.048	333	0.182	5.061
10	44	0.148	1.244	71	0.112	1.566	176	0.206	2.871	378	0.184	4.168
11	24	0.166	0.953	33	0.148	1.324	175	0.192	1.71	492	0.195	2.241
12	29	0.103	0.585	54	0.114	0.761	135	0.184	1.703	454	0.2	2.067
13	29	0.12	1.23	43	0.124	1.403	93	0.158	1.397	431	0.183	2.108
14	26	0.166	0.498	36	0.153	0.56	76	0.208	1.785	463	0.185	1.651
15	17	0.088	0.856	28	0.081	0.657	72	0.161	1.209	435	0.19	1.421
16	14	0.044	0.206	27	0.038	0.201	69	0.141	0.645	376	0.154	1.119
17	24	0.151	1	30	0.173	1.291	48	0.168	1.627	350	0.154	1.138
18	14	0.193	0.64	30	0.15	0.693	54	0.2	1.375	358	0.149	0.97
Xinyang	1990			2000			2010			2017
Ring	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS
1	1	0.968	297.44	1	0.968	298.24	1	0.968	298.72	1	0.968	299.2
2	4	0.221	188.2	2	0.455	396.72	2	0.565	406.48	1	0.928	835.84
3	77	0.194	11.684	63	0.19	15.743	14	0.23	86.389	13	0.254	102.572
4	280	0.168	2.074	263	0.174	2.393	121	0.176	8.169	64	0.213	20.765
5	265	0.18	1.567	246	0.181	1.911	147	0.188	4.716	152	0.213	6.945
6	268	0.162	1.799	262	0.159	2.037	192	0.187	3.734	190	0.202	5.799
7	236	0.168	2.043	220	0.167	2.398	182	0.165	3.78	183	0.175	5.863
8	207	0.162	1.594	200	0.164	1.756	177	0.174	2.434	132	0.218	5.673
9	180	0.156	0.95	174	0.16	1.041	115	0.207	2.387	124	0.198	3.614
10	189	0.169	0.782	186	0.172	0.819	150	0.191	1.636	124	0.223	3.52
11	158	0.156	0.687	158	0.156	0.693	143	0.158	1.328	123	0.207	3.148
12	212	0.122	0.69	210	0.122	0.709	145	0.136	1.834	91	0.195	6.082
13	153	0.154	0.656	152	0.155	0.681	139	0.166	1.275	94	0.243	4.294
14	111	0.19	0.817	112	0.191	0.826	112	0.184	1.007	87	0.217	3.062
Bozhou	1990			2000			2010			2017
Ring	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS
1	3	0.373	85.12	1	0.946	298.4	1	0.958	304.64	1	0.964	307.84
2	69	0.225	5.904	14	0.254	47.577	8	0.338	93.16	7	0.329	114.606
3	133	0.23	1.992	102	0.225	4.295	49	0.186	15.569	40	0.238	25.972
4	113	0.189	1.625	124	0.169	2.117	113	0.21	4.576	95	0.268	10.74
5	87	0.13	0.5	100	0.139	0.71	128	0.219	2.154	149	0.251	6.054
6	88	0.124	0.513	103	0.136	0.523	160	0.188	1.087	191	0.253	4.581
7	78	0.203	0.724	93	0.162	0.58	136	0.196	1.145	186	0.221	4.754
8	68	0.155	0.694	72	0.15	0.751	114	0.181	1.228	210	0.205	3.384
9	49	0.184	0.63	71	0.158	0.647	95	0.158	0.889	187	0.213	2.856
10	45	0.132	0.697	41	0.158	1.128	66	0.151	1.076	172	0.179	2.887
11	27	0.148	0.444	31	0.148	0.588	46	0.158	0.626	149	0.221	2.236
12	34	0.139	0.409	39	0.137	0.439	48	0.13	0.5	143	0.236	2.846
13	42	0.098	0.469	43	0.138	0.595	49	0.167	0.676	132	0.212	2.468
14	25	0.149	0.704	30	0.145	0.976	33	0.188	1.488	126	0.185	1.798

). According to the distribution trend of the scatter plot of landscape indices with distance, the software Origin 2021 was used to select the optimal function to fit (Figure 5 and

Table 5. Best-fitting function of landscape index with distance at optimal granularity.

City	Landscape Index	Function	Fitting Model	1 R2
Zhengzhou	NP	Sigmoid	y = (6.72 − 688.98)/(1 + x/16.75)6.35 + 688.98	0.975–0.994
	CONTIG_MN	Inverse S-shaped	y = (1 − 0.17)/(1 + e(17.33 ∗ (2x/7.09) − 1)) + 0.17	0.633–0.983
Xuzhou	NP	Sigmoid function	y = (14.51 − 383.51)/(1 + x/10.26)6.26 + 383.51	0.914–0.959
	CONTIG_MN	Inverse S-shaped	y = (1 − 0.25)/(1 + e(11.95 ∗ (2x/2.56) − 1)) + 0.25	0.889–0.983
Yancheng	CONTIG_MN	Inverse S-shaped	y = (1 − 0.19)/(1 + e(0.23 ∗ (2x/0.54) − 1)) + 0.19	0.892 (2017) 2
Xinyang	CONTIG_MN	Inverse S-shaped	y = (1 − 0.21)/(1 + e(12.54 ∗ (2x/4.9) − 1)) + 0.21	0.992–0.995
Bozhou	CONTIG_MN	Inverse S-shaped	y = (1 − 0.16)/(1 + e(7.3 ∗ (2x/3.14) − 1)) + 0.16	0.781–0.987
	MPS	Power	y = 85.1 ∗ x(−3.74)	0.984–0.999

¹ Range of fitting accuracy from 1990 to 2017. ² Fitting accuracy in 2017.

). The number of patches and the buffer distance from the city center were fitted to the sigmoid function, and only Zhengzhou and Xuzhou have higher fitting accuracy, reaching over 97%. From 1990 to 2017, for Zhengzhou and Xuzhou, where the buffer distance is within 9 km, the number of patches at the same rings decreased, which indicates that while the city continues to expand outward, the interior of the city becomes more compact. Moreover, the patch index of Xuzhou has intersections between the function curves of different years, with the corresponding patch numbers being 200 and 210. As the distance from the city center to the outskirts increases, the mean contiguity index of Zhengzhou, Xuzhou, Xinyang, Bozhou, and Yancheng showed a downward trend as a whole and stabilized at 0.17, 0.25, 0.2, 0.2, and 0.15, respectively, with similar trends to the distribution of the inverse S-shaped function (Equation (3)), After fitting with this function, the accuracy reaches more than 63%; the mean contiguity index was well fitted with the inverse S-shaped function with an accuracy of over 99% in Xinyang. The mean contiguity index is fitted to the power functions in Bozhou and shows a generally decreasing trend and converged to 0. However, the number of patches and the mean patch size in Yancheng are not fitted with the S-shaped and power functions.

In summary, the number of patches is positively correlated to the buffer distance from the city center, and the interval between the fitted curves increases with time. The mean contiguity index and the mean patch size are negatively correlated to the buffer distance from the city center. In 1990–2017, the number of patches gradually decreased in the inner circle and increased in the outer circle. Compared with the outer circle, the core area of the city became more compact as the patches gradually merged. Among the three fitting curves for the landscape indices and buffer distance, 2000 was an inflection year, before which the similarity of the landscape pattern was high.

3.3. Urban Land Density in Concentric Rings at the Optimal Granularity

According to the determined optimal granularity, the urban land density of each ring of the buffer zone in 1990, 2000, 2010, and 2017 in the five cities was calculated and fitted with the inverse S-shaped function, and the overall accuracy was more than 97%.

Table 6. Parameters of urban land density functions at optimal granularity.

City	Period	α	c	D	R2
Zhengzhou	1990	5.273	0.116	13.059	0.994
	2000	5.158	0.130	15.376	0.994
	2010	4.233	0.144	21.804	0.992
	2017	4.106	0.244	28.311	0.987
	Mean	4.693	0.159	19.638	0.992
Xuzhou	1990	3.498	0.103	8.087	0.986
	2000	3.239	0.113	9.753	0.989
	2010	2.807	0.110	13.837	0.985
	2017	2.764	0.083	19.145	0.981
	Mean	3.077	0.102	12.706	0.985
Yangcheng	1990	2.943	0.003	4.028	0.995
	2000	5.090	0.012	5.947	0.997
	2010	3.656	0.043	8.1528	0.978
	2017	2.834	0.068	11.958	0.971
	Mean	3.631	0.032	7.521	0.985
Xinyang	1990	4.189	0.047	6.466	0.989
	2000	4.529	0.051	6.786	0.987
	2010	4.163	0.055	7.921	0.987
	2017	3.779	0.074	9.357	0.983
	Mean	4.165	0.057	7.633	0.987
Bozhou	1990	2.961	0.010	3.770	0.996
	2000	4.417	0.011	5.009	0.998
	2010	4.013	0.017	6.049	0.998
	2017	3.084	0.071	7.825	0.985
	Mean	3.619	0.027	5.663	0.994

illustrates the three model estimation parameters fitted by the inverse S-shaped function. The parameter α is the slope of the inverse S-shaped function; the larger the value, the more compact the urban expansion is. From 1990 to 2017, the α mean of Zhengzhou was the largest, reaching 4.69, and the α mean of Xuzhou was the smallest at only 3.08. In general, the urban expansion of Zhengzhou continued to be compact, and Xuzhou showed spreading and expansion characteristics. The α values of Zhengzhou, Xuzhou, and Xinyang decreased with time, which indicates that all experienced extensive expansion. During this period, the α values of Yancheng and Bozhou first increased and then decreased, which indicates that the urban expansion changed from being compact to extensive. The parameter c represents the land density in the urban fringe area and reflects the linked development of the city with the surrounding towns and rural areas. From 1990 to 2017, the c value of the five cities increased, and that of Zhengzhou was the largest and showed the strongest linkage effect. The parameter D represents the radius of the urban area. The D values of Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou increased from 13.06, 8.09, 4.03, 6.47, and 3.77 km in 1990 to 28.31, 19.15, 11.96, 9.36, and 7.83 km in 2017, representing increases of 117%, 137%, 197%, 45%, and 108%, respectively.

Scatter plots and fitted curves in each city are shown in Figure 6. From 1990 to 2017, urban land density increased, and the urban form became more compact. Zhengzhou is the most compact city. The interval between the fitting curves of urban land density reflects the urban expansion rate. The intervals between the land density curves of the five cities from 2010 to 2017 are much larger than those from 1990 to 2000. The rapid economic growth in the later period led to the rapid urban expansion (Figure 6f). Zhengzhou, Xuzhou, and Yancheng expanded rapidly, Xinyang and Bozhou expanded relatively slowly, and Xinyang was generally unchanged from 1990 to 2000.

According to the inverse S-shaped function of each city, the radii of the urban land density at 75%, 50%, and 25% are defined as the urban core area, the near urban area, and the far urban area (Figure 7), respectively. The core, near urban, and far urban areas of the five cities in Figure 8 all expanded rapidly from 1990 to 2017, with the fastest expansion rate observed in the far urban areas. Zhengzhou has the widest expansion range and showed the fastest expansion rate, from 5.38, 6.86, and 8.66 km in 1990 to 11.72, 16.47, and 20 km in 2017, reaching rates of 0.198, 0.300, and 0.354, respectively. Xinyang and Bozhou expanded relatively slowly during this period, as the expansion rates only reached 0.031, 0.049, and 0.070, and 0.046, 0.070, and 0.098, respectively.

3.4. Landscape Patterns of Urban Expansion at Optimal Granularity

The patch number, mean contiguity, and mean patch size landscape indices are calculated at the optimal granularity in Appendix A and shown in Figure 5. It can be seen that in the inner ring of the buffer zone, the city has better connectivity and high compactness, and the outer periphery shows a trend of increasing fragmentation. Zhengzhou and Xuzhou as well as Xinyang and Bozhou have similar distribution laws in their landscape indices, which indicate that there are certain similarities in urban expansion between cities of the same level and between small- and medium-sized cities in general.

The α means of Zhengzhou and Xinyang are larger than those of Yancheng, Bozhou, and Xuzhou, which indicate that the expansion patterns of Zhengzhou and Xinyang are more compact than other cities (Table 6). The c of Bozhou is the smallest, which indicates that large- and medium-sized cities can drive the greater expansion of the surrounding areas to a greater degree than small cities. As for parameter D, the urban radii of small cities are smaller than those of large- and medium-sized cities, and their expansion rate is slower. The D values of all five cities are constantly increasing, and the urban areas show a radial outward expansion.

The three large cities of Zhengzhou, Xuzhou, and Yancheng, and the two small- and medium-sized cities of Xinyang and Bozhou, have similar urban land density curves (Figure 6). According to the interval between the curves, the expansion rate of large cities is higher than that of small- and medium-sized cities. By analyzing the node radii of the core, near urban, and far urban areas defined by urban land density, the growth rate of the urban area node radius corresponding to large cities is significantly higher than that of small- and medium-sized cities (Figure 7 and Figure 8).

4. Discussion

4.1. Determination of Optimal Granularity for Urban Expansion Analysis

By analyzing the landscape indices in 1990, 2000, 2010, and 2017, the first scale domain of typical cities in the Huaihe River Basin was 30~60 m, and the optimal granularity sizes of Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou were determined by the area loss evaluation method using 60 m, 50 m, 40 m, 40 m, and 40 m, respectively. Li et al. [62] studied the Jiawang mining area in Xuzhou City and determined that 50~60 m is the optimal granularity size range, which is consistent with the results of our study. Tian and Liu [63,64] selected 50 m as the optimal landscape granularity of Yancheng City, which slightly differs from the 40 m granularity used in our study but is still in the range of the first scale domain. Moreover, they focused on the coastal wetland landscape of Yancheng [65], which differs from the urban landscapes we take as our research setting, which verifies our results to a certain extent.

4.2. Urban Landscape Variation in Different Watershed Locations

At the optimal landscape granularity, cities in different locations of the Huaihe River basin have great similarity in three landscape indices (i.e., the number of patches, mean contiguity index, and mean patch size), but there are also slight differences related to the defined urban boundaries [35] and geographic location. The number of patches and the mean patch size are similar in different cities and show an increasing and decreasing trend, respectively (see

Table A2. Landscape Index of Yancheng City under the 30 m Land Cover Dataset in China from 1990 to 2019.

Yancheng	1990			2000			2010			2017
Ring	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS	NP	CONTIG_MN	MPS
1	1	0.967	310.720	1	0.969	313.280	1	0.967	312.000	1	0.966	311.360
2	6	0.264	128.320	3	0.314	290.507	3	0.318	301.333	2	0.477	451.440
3	97	0.222	6.037	33	0.269	31.433	15	0.293	86.656	8	0.360	173.400
4	174	0.202	1.528	155	0.285	4.087	74	0.300	15.840	47	0.307	30.557
5	173	0.175	1.383	166	0.244	3.897	130	0.294	9.077	121	0.309	12.517
6	181	0.162	1.115	201	0.236	2.298	170	0.243	6.369	142	0.297	11.367
7	209	0.117	0.589	240	0.179	0.992	264	0.236	3.196	234	0.252	6.371
8	164	0.134	0.803	196	0.183	1.194	232	0.215	3.550	229	0.226	6.165
9	217	0.128	0.882	231	0.184	1.259	332	0.205	1.947	286	0.245	4.991
10	206	0.152	1.348	219	0.177	1.862	292	0.223	2.485	315	0.245	4.462
11	258	0.154	0.736	245	0.198	1.151	325	0.236	1.487	399	0.270	2.635
12	293	0.148	0.805	280	0.175	1.291	350	0.195	1.548	425	0.236	2.217
13	278	0.150	0.962	286	0.165	1.249	327	0.185	1.394	388	0.230	2.191
14	304	0.132	0.597	308	0.183	0.850	340	0.205	1.143	434	0.239	1.681
15	307	0.132	0.663	316	0.167	0.890	344	0.181	1.052	451	0.208	1.530
16	384	0.122	0.493	393	0.146	0.614	419	0.160	0.720	485	0.193	1.124
17	417	0.130	0.596	407	0.150	0.802	450	0.158	0.891	511	0.195	1.361
18	436	0.121	0.575	432	0.171	0.796	458	0.194	1.055	520	0.221	1.409

), which indicates that cities in different locations expand over time. In terms of the mean contiguity index (Figure 5), the five cities in the upper, middle, and lower reaches are in a decreasing trend, and Xuzhou has the largest final stable value, the highest proximity, and the best landscape connectivity. Xuzhou is located in the Yishusi River Basin and is characterized by a flat topography and the Beijing–Hangzhou Grand Canal crossing from north to south, and a modern three-dimensional transportation system with railroads, airlines, highways, waterways, and pipelines. To our surprise, the landscape pattern of Yancheng is much different than those in other cities. As a coastal city, Yancheng is located in the lower reaches of the Huaihe River Basin wetlands [65,66], so its landscape pattern differs significantly from that of other cities (Figure 5).

4.3. Urban Land Density among Differently Sized Cities

The urban land density functions of different cities are similar before 2000 and much different when compared to the standard inverse S-shaped function. From 1990 to 2000, the transportation facilities in Zhengzhou were in the initial stage of their development, and the urban land expansion was relatively slow. In the “Eleventh Five-Year Plan,” Zhengzhou was established as an important central city and land transportation hub in central China [67], and as a result its urban land density function gradually approached the standard inverse S-shaped function. As an industrial and mining city, Xuzhou relied on resource exploitation in the early periods to accelerate urban development, and the distribution of cities was more compact with large α values, while in the mid-late stage, it experienced resource depletion and economic transformation [68], the damaged ecological environment became a heavy burden that discourages urban development [69], and urban land expansion slowed down and became less compact. Yancheng, located in the lower reaches of the Huaihe River Basin, expanded slowly before 2002 due to a lack of railroad access, but expanded with the largest urban growth rate in the later periods because of its formation of an integrated transportation network that incorporates land, sea, and air modes of transport. As a city in the upper reaches of the Huaihe River Basin, Xinyang’s urban land density curves basically overlapped with the smallest urban expansion rate from 1990 to 2000, and its urban expansion rate gradually increased due to it becoming a hub city in the Huaihe River Basin. Bozhou is a small city that exhibits significant differences between the urban land density distribution and the standard inverse S-shaped function in the early stages. Zhengzhou, Xuzhou, and Yancheng are similarly sized, as are their urban land density curves. The medium-sized city of Xinyang and the small-sized city of Bozhou have similar urban land density functions due to their locations and similar urban forms.

There are obvious differences in the urban land density functions between large cities and small- and medium-sized cities [36]. The urban land densities of different cities were obtained by averaging the densities of large cities with similar urban land density curves, as well as that of small- and medium-sized cities with similar buffer zones (Figure 9). From 1990 to 2017, the land densities of cities of different sizes gradually increased, but the urban expansion rate slowed from 1990 to 2000, which differs from the standard inverse S-shaped function. Compared with small- and medium-sized cities, large cities expand more rapidly and their land use density tends to approach the standard inverse S-shape, while the urban land density of medium- and small-sized cities tends to decline linearly until reaching a stable value. This finding is consistent with the results of Haikai et al. [70], who studied urban expansion along the Belt and Road.

4.4. Comparison of Different Datasets

By analyzing the parameters of urban land density formula at the optimal granularity, the urban spatial of Yancheng [71] is much different than those in other cities. Here, we calculated urban land density (Figure 5 and Figure 10) using the impervious surface data in 1990, 2000, 2010, and 2017 extracted from the 30 m land cover dataset (1.0.0) in China from 1990–2019 for validation [55]. Although urban land density shows a more remarkable pattern than the results using the data in this paper (Table 6), the accuracy has not improved much and remains at the same level (

Table 7. Parameters of urban land density functions in the 1990–2019 dataset under optimal granularity.

City	Period	α	c	D	R2
Yancheng	1990	5.402	0.034	5.434	0.998
	2000	4.744	0.050	6.880	0.991
	2010	3.624	0.066	9.045	0.985
	2017	3.017	0.091	11.083	0.979
	Mean	4.197	0.060	8.111	0.988

). The data source may affect the calculation results to some extent, but the main reason lies in the urban function and landscape type.

4.5. Limitations and Uncertainties

In order to reflect the urban expansion characteristics of the Huaihe River Basin, the selection of sample cities is crucial. This study first considered the different scale levels of the cities, but the megacity Nanjing, which is the main body of urban construction, is not within the study area [72]. Therefore, three scale cities of large-, small-, and medium-size were selected for the sample. Due to the different size distribution of cities in different watershed locations, most of the cities in the upper reaches are small- and medium-sized cities, while most of the cities in the middle and lower reaches as well as in the Yishushi River region are large- and medium-sized cities. Therefore, considering the location of the city’s watershed, the functional characteristics of cities (Table 1), and the conclusion of previous studies that large cities are more suitable for urban land density models [70], five sample cities were finally identified: Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou.

Finding the optimal granularity is the motivation for studying urban expansion in differently sized cities. However, there are some limitations in terms of our selection of landscape indices and granularity sizes [73], leading to a certain subjectivity in the determination of the optimal granularity. Previous studies have typically used land use and land cover data interpreted by remote sensing images [60], and the landscape indices were selected from patches, classes, and landscapes levels [74,75]. However, given that we only used urban impervious surface data [26], we could only select landscape indices from patch levels; the index types were limited by the data, and six landscape indices were selected to determine the optimal landscape granularity. This may result in our results not fully reflecting the landscape pattern characteristics and deficiencies in generalizability.

To ensure the full use of the data, most researchers resample raster data into data with different granularities [60,63]. In our study, we used the original resolution as the starting point to generate eight images of different granularities at an interval of 10 m [45]. We effectively avoid computational redundancy due to the small scale while increasing the error in determining the first scale domain.

Urban boundaries are defined as the area that includes continuous functional urban areas and the outer ring road of the city while excluding satellite cities located far from the central urban core [31,35]. However, when using the urban land density method to analyze urban expansion, the delineation of urban boundaries is not precise enough, which makes the results uncertain to a certain degree.

5. Conclusions

This study constructed an optimal granularity selection method based on scale transformation and area loss evaluation to determine the optimal granularities to use in the analysis of the urban expansion of differently sized cities in the Huaihe River Basin. The results showed that landscape indices could indicate the scale effect with different granularities, and the first scale domain of the landscape indices helps to determine the optimal granularity. The total class area, largest patch index, and perimeter-area fractal dimension have obvious scale inflection points, while the mean patch size, landscape shape index, and patch density have nonsignificant scale inflection points. We find that the optimal granularities of Zhengzhou, Xuzhou, Yancheng, Xinyang, and Bozhou are 60 m, 50 m, 40 m, 40 m, and 40 m, respectively.

The urban landscape pattern and urban land density calculated using the optimal granularity can effectively reveal the urban expansion laws of differently sized cities. Compared with small- and medium-sized cities, large cities have faster expansion, stronger linkage development with surrounding areas, and a higher degree of urban centralization. Moreover, urban expansion was influenced by urban locations and functions. Medium- and small-sized cities located in the upstream area expanded slowly, while large cities located in the mid- and downstream areas were also affected by their urban function. As a national center city, Zhengzhou has the fastest and most compact expansion; as a resource-based city, Xuzhou is characterized by sprawling expansion; as a downstream city, Yancheng showed compact expansion in the early stages and sprawling expansion in the later stages. These findings reveal the importance of considering optimal granularity in urban landscape and expansion research so that policymakers can adopt appropriate practices for cities of different sizes, locations, and functions in watershed urbanization.