The spatial-temporal evolution of urban systems is a complex scale-free dynamic process, which can be described quantitatively by allometric scaling index. In this study, the multi-scaling allometric analysis method was employed to analyze the relative development characteristics and the spatial heterogeneity pattern of the main cities in the Beijing-Tianjin-Hebei region based on the calibration results of the nighttime light data from 1992 to 2013. The main findings are as follows: 1) The limitations on spatial development of big cities in the Beijing-Tianjin-Hebei region were increasing. Although the absolute development levels of big cities such as Beijing, Tianjin, and Tangshan were higher than medium-sized and small cities, large cities were close to the limit of environmental carrying capacity; smaller cities such as Sanhe, Qian'an, and Langfang had grown rapidly in the 22 years. 2) Cities with relatively high growth advantage show a zonal distribution from northeast to southwest. These small cities are located in the space between the big cities. Two principal conclusions can be drawn as below: 1) The trend of urban change in Beijing, Tianjin, and Hebei is relatively balanced. Heterogeneity of the spatial structure has gradually weakened, and the development of the whole urban system tends to evolve into a relatively homogeneous state. 2) The key of spatial optimization in the Beijing-Tianjin-Hebei region is to unify the two extremes of cites. The large cities with absolute high development levels and the small cities with relatively high growth rates should be integrated into a self-organized framework. The nighttime light data can be used to characterize the allometric scaling relations between elements of urban systems and to explain the formation mechanism of spatial heterogeneity.

One of the indicators of regional integration of urban and rural areas is the integration of the structure of systems of cities and towns. This process can be described and evaluated using the concept of scaling. Fractal geometry is one of the powerful tools for scaling analysis. An important parameter of geographic spatial distribution characteristics is fractal dimension. Based on data derived from remote sensing images and census data, this study carried out fractal analysis, rank-size distribution analysis, and allometric scaling analysis of cities and urban system in the Beijing-Tianjin-Hebei region. The aim was to explain the process of urban growth in the region from 1995 to 2013. The results show three characteristics of urban form and growth: 1) Both the spatial structure and the rank-size distribution of the cities in the Beijing-Tianjin-Hebei region are of self-affine pattern, indicating bi-fractal property. 2) The relationship between urban population and urban area of the Beijing-Tianjin-Hebei region indicates a false linear correlation. 3) With the change of the urban system, the self-affine bi-fractal structure evolved gradually into a self-similar fractal structure. The main conclusions are as follows: 1) There is a structural incongruity in the system of cities and towns in the Beijing-Tianjin-Hebei region. The urban hierarchy takes on a dual structure, but the direction of urban change shows a significant trend of internal structure integration. 2) Land use in large cities is not intensive enough. The unordered expansion of urban fringe led to the waste of land resources. Planners and local governments should make use of the characteristics and trends of change of the urban system to formulate planning schemes and management measures.

Urban growth and form are important contents of geographic research on sizes and shapes. Fractal dimension is an effective scaling parameter to describe urban form and reflect urban growth. Based on remote sensing data of construction land in 2000, 2005 and 2010, this study analyzed the spatial pattern and change of cities and towns in the Beijing-Tianjin-Hebei region. Fractal measures, including radial dimension and the corresponding concept of scaling range, were applied. The main results are as follows: 1) The first scaling area and its growth rate of Beijing are the largest in the Beijing-Tianjin-Hebei urban system, producing a shadow effect on the surrounding cities. 2) On the whole, the farther from Beijing, the smaller the scope of the first scaling range of other cities. 3) For almost all the cities in the Beijing-Tianjin-Hebei region, the first scaling areas are overfilled by construction land. 4) Economic development level has the greatest impact on the overall urban construction land expansion in the region, but the driver of urban construction land expansion in Beijing has changed from economic factors to population factors. Based on these findings, several conclusions can be drawn: 1) Beijing has dual effects in the process of urban development in the region, including the primary city effect, and the shadow effect. While Beijing drives the development of the Beijing-Tianjin-Hebei region, it also inhibits the growth of some other cities. 2) The central part of each city in the study region is too compact, but the development of the peripheries is relatively disorderly, and the main city areas and outskirts lack integration. 3) Population may become the key dynamics of the urban change in the Beijing-Tianjin-Hebei region. The principal role of economic return growth may be replaced by the economies of scale based on urban population agglomeration in the future. These results and conclusions may help the research community and government authorities understand the status quo and future development trend of urbanization in the Beijing-Tianjin-Hebei region from a new perspective.

Cities and urban systems both bear scale-free properties, from which no characteristic scales can be found for mathematical modeling and quantitative analysis. Therefore, fractal geometry is useful for making scaling analysis. Complex urban systems cannot be effectively described by simple fractal models, but can be characterized by multifractal theory. This paper is devoted to exploring the spatiotemporal features of urban change in the Beijing-Tianjin-Hebei region from 1995 to 2013. Using multifractal parameter spectrums, we can reveal the spatial dynamics of urbanization from the aspects of urban form and urban system. The main findings are as below: 1) The spectral curves of global fractal dimension are abnormal. If q>1 and q→∞, the spectral lines quickly converge to horizontal lines; when q<0 and q→-∞, the spectral lines quickly surpass the upper limit of fractal dimension, 2, which represents Euclidean dimension of embedding space. 2) The spectral curves of local fractal dimension are also not entirely normal. The peaks of the f(α) curves incline to the left, and the left ends of the curves are higher than the right ends. The problem lies in that the curves go beyond the maximum value of 2. 3) Fractal dimension growth curves can be described by the quadratic logistic function. Capacity parameters and inflection points of different fractal dimension growth curves are different. The main conclusions are as follows: 1) The urban fringes are disorderly developed, while the central areas of the main cities in the Beijing-Tianjin-Hebei region is overfilled with construction land, leaving little buffer space. 2) The main mode of urban growth is to expand to the outside region, but there are signs of central agglomeration in the total construction land of Hebei Province. 3) Land use of the main cities is close to saturation, and the speed of land expansion has peaked for Beijing and Tianjin, but not in Hebei Province yet. In short, it is necessary to optimize the land use structure in the Beijing-Tianjin-Hebei region by city planning.

Fractal geometry provides a powerful tool for scale-free spatial modeling and analyses in geography. However, a number of basic concepts are puzzling. The three common fractals, that is, monofractal (unifractal), multifractals, and self-affine fractal, are often misunderstood by students of geography. This article clarifies some confusing fractal concepts for urban fractal modeling and fractal dimension analysis. Using simple mathematical models based on three growing fractals that bear an analogy to urban growth, we can distinguish the three types of common fractal structure. The similarities and differences between monofractal, multifractals, and self-affine fractal are as follows: 1) A monofractal is a simple self-similar fractal that bears only one scaling factor (scaling ratio), and a multifractal object is a complex fractal system that bears at least two scaling factors for different parts. Each scaling factor dominates all different scales and is independent of directions and levels. 2) A self-affine fractal bears different scaling factors in different directions of growth or at different levels of scales. The basic feature of self-affine growing fractal is anisotropy, which differs from the isotropic self-similar growing fractals. 3) Both self-affine fractal and multifractals may possess two scaling factors, but there are essential differences between self-affine fractals and multifractals. A self-affine fractal often takes on the form of bi-fractals, which can be reflected by two scaling ranges on a log-log plot. However, there is only one scaling range for a multifractal pattern. As an example, two-scaling fractal modeling is applied to the rank-size distributions of cities to illustrate the concept of urban multifractals. By comparison with these multifractal models, we can better understand monofractals and self-affine fractals in geographical research.

In order to achieve harmonious ecological and economic development in urban agglomerations, it is important to explore the trade-offs between environmental protection and economic development, and use this knowledge to optimize land use allocation. This study aimed to simulate land use changes in the Beijing-Tianjin-Hebei urban agglomeration with different goals and under different scenarios in 2025 to identify the optimal land use allocation strategies based on the trade-offs between ecological and economic benefits. In order to meet the land use demands for environment-friendly development in the Beijing-Tianjin-Hebei urban agglomeration, we developed two optimization goals—ecosystem services value maximization and economic value maximization, and four land use scenarios—environmental protection, balanced development, food security, and economic development focus. A CLUE-S model was built to simulate and predict the optimal land use allocation strategy. The results show that the optimal land use allocations with the ecosystem services maximization goal were very different comparing to that with the economic value maximization goal. The ecosystem services value is estimated to be approximately 1442.36 billion Yuan with the ecosystem services maximization goal and under the environmental protection scenarios, more than that with the economic value maximization goal and under the same scenario. Spatially, the increase of ecologically beneficial land-use types, including forest land and grassland, is more often seen in the Bashang Plateau, Yanshan Mountains, and Taihang Mountains. The increase of water areas often occurs in coastal regions in the east. There are significant trade-offs between ecosystem services value maximization and economic value maximization. The results of this trade-off analysis can provide a basis for future ecological projects in the Beijing-Tianjin-Hebei urban agglomeration.

With regional integration continuously developing, it has become essential to establish good governance mechanism in regional development. Due to the strategic status of the Beijing-Tianjin-Hebei region, its collaborative governance has been even more important, but the region is also facing a number of challenges. In order to understand better the characteristics of regional governance in the Beijing-Tianjin-Hebei region and to propose some optimization approaches that can support the implement of regional planning, this study conducted a comparative analysis and built a three-dimensional research framework including participants, means of governance, and cooperation mechanisms. On the basis of this, we summed up the characteristics and pattern of change of regional governance in the Beijing-Tianjin-Hebei region, the Berlin-Brandenburg region, the Tokyo metropolitan area, and the Paris metropolitan area, especially with regard to their differences. The three conclusions are as follows: 1) Multi-subjects participation has been the essential characteristics of regional governance, whose authority-responsibility relationships must be unambiguous. In practice, multiple players have participated in the regional governance in the Beijing-Tianjin-Hebei region, but the relationships among them need to be clarified. Founding a regional institution would be a good chance to straighten these relationships. 2) Only when the administrative means, market mechanisms, and legislation are interrelated and interact positively, can regional governance be effective. However, the governance structure of the Beijing-Tianjin-Hebei region, which consists of good administrative means, limited market mechanisms, and inadequate legislation, shows some limitations. To fix the problems, enhancing legislation system shall be the priority and this in turn can promote the interaction between the government and the market. 3) An efficient multilateral consultation mechanism is indispensable, which could support decision making and dispute arbitration. In this respect, the Beijing-Tianjin-Hebei region has already had a good decision-making mechanism, but there are some inadequacies in dispute arbitration and supervision. It is necessary to speed up and improve the overall coordination mechanism, which can be applied to all aspects of the governance practice.

Beijing-Tianjin-Hebei regional governance is a series of effective measures and is associated with governments' collaborative development process that has changed from the government level control to various stakeholders coordinated governance, from top-down competition and cooperation to synergistic collaboration of all levels. After more than 30 years' efforts, the academic community and the government have obtained a rich set of research achievements in the regional governance of the Beijing-Tianjin-Hebei region. In order to improve the regional governance effect of the Beijing-Tianjin-Hebei region, this article compiles the relevant regional studies since 1984 and attempts to clarify the context and changes of regional governance research of the Beijing-Tianjin-Hebei region from the spatial and temporal aspects, and analyzes the governance model, coordination system, and development strategy of the current Beijing-Tianjin-Hebei regional governance approach. The process of coordinating the governance of the Beijing-Tianjin-Hebei region is the interaction and integration of academia and the government, and the role of the government has been dominant. Future research will deepen and refine the understanding on the governance subjects, governance mechanisms, governance effectiveness evaluation, and coordinated development of culture, health care, and pension system.