信阳城市人口—城区用地异速生长分析

doi:10.11820/dlkxjz.2014.08.006

摘要/Abstract

摘要：

城市人口规模和用地面积随着时间的改变过程理论上服从异速生长定律,即在一定时空范围内表现为幂指数关系,并且标度指数小于1。但由于种种原因,中国的统计数据大多不满足纵向异速标度关系,或者标度指数严重异常。为深入研究这一问题,借助最小二乘法和对数线性回归分析技术,基于信阳的人口普查数据和城市用地现状图资料,开展城市人口和城市用地面积的标度分析,发现城市生长长期服从纵向异速生长定律,可用幂函数描绘,并且标度指数(约为0.86)接近于理论预期值(0.85)。然而,由于近年的“造城运动”,这种标度关系遭到破坏,城市人—地关系出现混乱。因此,揭示城市演化规律的前提是数据质量的保证,而人文系统的规律也会因为人为的因素而暂时破坏。本文提供了一个城市纵向异速生长及其标度破坏的简明案例,并给出了估计和预测信阳城市人口和用地的数学模型,其计算结果可以作为了解同类城市人—地关系的演化进程和未来趋势的重要参考。

关键词: 异速生长, 异速标度, 分维, 标度间断, 城市人—地关系, 信阳

Abstract:

The relationship between urban population and construction land area is supposed to follow the law of allometric growth, which is based on exponential growth or distribution. However, if we apply the allometric scaling law to Chinese cities using data from the statistical yearbooks of China, the relationship is often unclear or unconvincing, possibly due to the quality of the statistical data used. In this study, the ordinary least square method and log-linear regression analysis are employed to make a longitudinal allometric analysis of urban evolution of Xinyang, a medium-sized city of Henan Province, China. Population of the urban area (which is greater than the non-agricultural population of the same city) was estimated by using the census data from multiple years; the area of urban construction land was estimated using the land-use maps. The quality of these data is clearly higher than those provided in the statistical yearbooks. The result of the analysis shows that from 1949 to 2004, the urban population and area of construction land in Xinyang followed the allometric scaling law. During the period between 2007 and 2013, the scaling relation was disrupted due to the "city-making movement" in the context of an overheated economy based on real estate development and rapid urbanization. The following conclusion can be drawn: the urban evolution of Chinese cities follows the allometric growth law, but the allometric scaling can be disturbed by government policies in a largely command and control economy. The significance of this work lies in that, first, it provides a typical case of longitudinal allometry of China's cities for urban studies; second, it gives a set of models that can be used to estimate and project population size and urban land area of cities like Xinyang; and third, it lays a foundation for future allometric studies based on logistic growth rather than exponential growth.

Key words: allometric growth, allometric scaling, fractal dimension, scaling breaking, urban human-environment relation, Xinyang

中图分类号:

K901.8

陈彦光, 张莉. 信阳城市人口—城区用地异速生长分析[J]. 地理科学进展, 2014, 33(8): 1058-1067.

Yanguang CHEN, Li ZHANG. An allometric analysis of the scaling relations between population and urban area of Xinyang[J]. PROGRESS IN GEOGRAPHY, 2014, 33(8): 1058-1067.

图/表 7

表1

图1

图2

图3

图4

表2

信阳城市人口和城市建设用地面积估计值和预测值"

年份 n	时序 t	人口规模P_t/万人	建设用地面积A_t/km²
年份 n	时序 t	Logistic预测值	Logistic预测	二次logistic预测	异速生长预测1	异速生长预测2
1949	0	3.76	4.63	6.14	4.70	4.30
1950	1	3.94	4.82	6.14	4.89	4.50
1951	2	4.12	5.02	6.15	5.09	4.70
1952	3	4.32	5.23	6.17	5.30	4.91
1953	4	4.53	5.44	6.21	5.52	5.14
1954	5	4.74	5.67	6.24	5.74	5.37
1955	6	4.97	5.90	6.29	5.98	5.61
1956	7	5.21	6.15	6.35	6.22	5.87
1957	8	5.46	6.40	6.42	6.48	6.13
1958	9	5.72	6.67	6.49	6.74	6.41
1959	10	5.99	6.94	6.58	7.02	6.70
1960	11	6.27	7.23	6.68	7.30	7.00
1961	12	6.57	7.53	6.78	7.60	7.32
1962	13	6.89	7.84	6.90	7.91	7.65
1963	14	7.21	8.16	7.03	8.23	8.00
1964	15	7.56	8.50	7.18	8.57	8.36
1965	16	7.91	8.85	7.34	8.92	8.73
1966	17	8.29	9.21	7.51	9.28	9.12
1967	18	8.68	9.59	7.69	9.66	9.53
1968	19	9.09	9.98	7.89	10.05	9.96
1969	20	9.52	10.39	8.11	10.46	10.41
1970	21	9.97	10.81	8.34	10.88	10.88
1971	22	10.44	11.26	8.59	11.32	11.36
1972	23	10.94	11.71	8.87	11.78	11.87
1973	24	11.45	12.19	9.16	12.26	12.40
1974	25	11.99	12.69	9.48	12.75	12.96
1975	26	12.55	13.21	9.82	13.26	13.53
1976	27	13.14	13.74	10.18	13.80	14.14
1977	28	13.76	14.30	10.58	14.35	14.77
1978	29	14.40	14.88	11.00	14.93	15.42
1979	30	15.08	15.48	11.46	15.53	16.11
1980	31	15.78	16.11	11.95	16.15	16.82
1981	32	16.52	16.76	12.48	16.80	17.56
1982	33	17.29	17.43	13.05	17.47	18.34
1983	34	18.09	18.13	13.67	18.16	19.15
1984	35	18.93	18.86	14.33	18.89	19.99
1985	36	19.80	19.61	15.04	19.63	20.87
1986	37	20.72	20.40	15.81	20.41	21.78
1987	38	21.67	21.21	16.64	21.22	22.73
1988	39	22.67	22.06	17.53	22.06	23.73
1989	40	23.71	22.93	18.50	22.93	24.76
1990	41	24.80	23.84	19.54	23.83	25.83
1991	42	25.93	24.79	20.67	24.76	26.95
1992	43	27.11	25.77	21.89	25.73	28.12
1993	44	28.34	26.78	23.20	26.73	29.33
1994	45	29.63	27.83	24.63	27.77	30.59
1995	46	30.96	28.92	26.17	28.85	31.90
1996	47	32.36	30.05	27.83	29.96	33.27
1997	48	33.81	31.22	29.64	31.11	34.68
1998	49	35.32	32.43	31.59	32.31	36.16
1999	50	36.90	33.69	33.71	33.54	37.69
2000	51	38.54	34.99	36.00	34.82	39.27
2001	52	40.24	36.34	38.48	36.14	40.92
2002	53	42.02	37.73	41.17	37.51	42.63
2003	54	43.86	39.17	44.08	38.92	44.41
2004	55	45.78	40.66	47.24	40.38	46.25
2005	56	47.77	42.20	50.65	41.89	48.16
2006	57	49.84	43.79	54.34	43.45	50.14
2007	58	51.99	45.44	58.33	45.05	52.19
2008	59	54.22	47.14	62.64	46.71	54.31
2009	60	56.53	48.89	67.30	48.42	56.51
2010	61	58.93	50.70	72.32	50.18	58.79
2011	62	61.41	52.57	77.72	52.00	61.14
2012	63	63.99	54.50	83.53	53.87	63.57
2013	64	66.65	56.49	89.77	55.79	66.08
2014	65	69.41	58.54	96.45	57.77	68.67
2015	66	72.26	60.66	103.59	59.81	71.35
2016	67	75.21	62.83	111.21	61.90	74.11
2017	68	78.25	65.08	119.30	64.05	76.96
2018	69	81.40	67.38	127.88	66.26	79.89
2019	70	84.64	69.76	136.94	68.53	82.92
2020	71	87.99	72.20	146.48	70.85	86.03
2021	72	91.44	74.71	156.47	73.24	89.22
2022	73	94.99	77.28	166.90	75.68	92.51
2023	74	98.64	79.93	177.72	78.18	95.89
2024	75	102.40	82.65	188.91	80.73	99.36
2025	76	106.26	85.43	200.41	83.35	102.91
2026	77	110.23	88.29	212.15	86.02	106.56
2027	78	114.30	91.22	224.08	88.74	110.29
2028	79	118.47	94.22	236.13	91.52	114.11
2029	80	122.75	97.29	248.21	94.36	118.02
2030	81	127.12	100.43	260.25	97.25	122.01

表2

图5

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