Measurement of Urban Economic Gravity of China’s Three Major Agglomerations and Its Implications for the Coordinated Development of the Beijing-Tianjin-Hebei Region

This paper adopts the perspective of urban economic linkage and the modified urban economic gravity model to conduct a comparative analysis of the economic gravity among cities in China’s three major urban agglomerations,including the Beijing-Tianjin-Hebei region,the Yangtze River Delta,and the Pearl River Delta.The results show that,despite the ever-tightening economic linkages among cities in the urban agglomerations,the development of the Beijing-Tianjin-Hebei region falls behind that of the Yangtze River Delta and the Pearl River Delta in terms of coordination,closeness,and balance.The economic linkages among cities in the Beijing-Tianjin-Hebei region are not as cohesive as they could be and display a significant“siphon effect”through Beijing and Tianjin as well as a prominently unidirectional economic flow.This study suggests that efforts should be put into directing the orderly flow of resources from Beijing and Tianjin to cities in Hebei and promoting a balanced economic flow among cities,thus facilitating the coordination of regional development.

Spatiotemporal Variations and Regional Transport of Air Pollutants in Two Urban Agglomerations in Northeast China Plain

Characteristics of air pollution in Northeast China(NEC) received less research attention in the past comparing to other heavily polluted regions in China.Spatiotemporal variations of six criteria air pollutants(PM10, PM2.5, SO2, NO2, O3 and CO) in Central Liaoning Urban Agglomeration(CLUA) and Harbin-Changchun Urban Agglomeration(HCUA) in NEC Plain were analyzed in this study based on three-year hourly observations of air pollutants and meteorological variables from 2015 to 2017.The results indicated that the annual mean concentrations of air pollutants are generally higher in the middle and southern regions in NEC Plain and lower in the northern region.Megacities such as Shenyang, Harbin and Changchun experience severe air pollution, with a three-year averaged air quality index(AQI) larger than 80, far exceeding the daily AQI standard at the first-level of 50 in China.The annual mean PM and SO2 concentrations decrease most significantly in NEC urban agglomerations from 2015 to 2017, followed by CO and NO2, while O3 shows a slight increasing trend.All the six pollutants exhibit obvious seasonal and diurnal variations, and these variations are dictated by local emission and meteorological conditions.PM2.5 and O3 concentrations in NEC urban agglomerations strongly depend on wind conditions.High O3 concentrations at different cities usually occur in presence of strong winds but are independent on wind direction(WD), while high PM2.5 is usually accompanied by weak winds and poor dispersion condition, and sometimes also occur when the northerly or southerly winds are strong.Regional transport of air pollutants between NEC urban agglomerations is common.A severe haze event on November 1–4, 2017 is examined to demonstrate the role of regional transport on pollution.

Impact of Anthropogenic Heat Release on Regional Climate in Three Vast Urban Agglomerations in China

We simulated the impact of anthropogenic heat release （AHR） on the regional climate in three vast city agglomerations in China using the Weather Research and Forecasting model with nested high-resolution modeling.Based on energy consumption and high-quality land use data,we designed two scenarios to represent no-AHR and current-AHR conditions.By comparing the results of the two numerical experiments,changes of surface air temperature and precipitation due to AHR were quantified and analyzed.We concluded that AHR increases the temperature in these urbanized areas by about 0.5℃-1℃,and this increase is more pronounced in winter than in other seasons.The inclusion of AHR enhances the convergence of water vapor over urbanized areas.Together with the warming of the lower troposphere and the enhancement of ascending motions caused by AHR,the average convective available potential energy in urbanized areas is increased.Rainfall amounts in summer over urbanized areas are likely to increase and regional precipitation patterns to be altered to some extent.

The spatial-temporal differentiation of green land use in Beijing-Tianjin-Hebei urban agglomeration

As the space carrier of the construction of ecological civilization, land's green and efficient utilization is an important guarantee for realizing national sustainable development. Based on traditional land evaluation, this paper scientifically defines the green land use, puts land as one of the production factors, and brings energy consumption, environmental pollution, etc. into the input-output system to measure the green land utilization efficiency of the urban construction land of Beijing-TianjinHebei Urban Agglomeration from 2006 to 2016. The study shows that the overall efficiency variation of the urban agglomeration is related with the land and environment policies. Efficiency of 2016 is higher than that of 2006, and energy and environment are the principal factors affecting the green land use. The efficiency of each city is positively correlated with its economic development, negatively correlated with the construction land expansion. Efficiency gaps in different cities are expanding.There is positive correlation with overall weak space between cities, and the partial spatial agglomeration phenomenon appears. Therefore, the green land use efficiency could be improved by improving land utilization efficiency, coordinating economic growth of construction land utilization with environmental protection and taking feasible ways to transregional renovation of the stock ecological land utilization, etc.

Impact of Anthropogenic Aerosols on Summer Precipitation in the Beijing–Tianjin–Hebei Urban Agglomeration in China:Regional Climate Modeling Using WRF-Chem

The WRF model with chemistry （WRF-Chem） was employed to simulate the impacts of anthropogenic aerosols on summer precipitation over the Beijing-Tianjin-Hebei urban agglomeration in China. With the aid of a high-resolution gridded inventory of anthropogenic emissions of trace gases and aerosols, we conducted relatively long-term regional simulations, considering direct, semi-direct and indirect effects of the aerosols. Comparing the results of sensitivity experiments with and without emissions, it was found that anthropogenic aerosols tended to enhance summer precipitation over the metropolitan areas. Domain-averaged rainfall was increased throughout the day, except for the time around noon. Aerosols shifted the precipitation probability distribution from light or moderate to extreme rain. Further analysis showed that the anthropogenic aerosol radiative forcing had a cooling effect at the land surface, but a warming effect in the atmosphere. However, enhanced convective strength and updrafts accompanied by water vapor increases and cyclone-like wind shear anomalies were found in the urban areas. These responses may originate from cloud microphysical effects of aerosols on convection, which were identified as the primary cause for the summer rainfall enhancement.

Dynamic Evaluation on Regional Tourism Competitiveness:Urban Agglomeration of Shandong Peninsula,Eastern China

The article establishes the appraisal index system for entire urban agglomeration and its interior cities individually,concretely including five aspects:driving forces for tourism development,the level of tourism development,tourism impacts,tourism economic connection and tourism contributions of different cities to the whole urban agglomeration.As tourism competitiveness has the characteristics of comprehensiveness,systematicness and dynamicness,the article attempts to apply the structural prediction means of system dynamics to evaluating tourism competitiveness,aiming to provide some research methods and analysis ideas for tourism competitiveness measurement and trends analysis in urban agglomeration.Taking Shandong Peninsula urban agglomeration as the study area,the article simulates and analyzes the tourism competitiveness trend of the whole region and its interior cities from 2005 to 2020,and the result reflects that integrated development and regional combination of tourism are important means to upgrade tourism competitiveness in this region.

Impact of Climate Change on Urban Agglomerations in China’s Coastal Region

Climate change and urbanization issues are the two key factors that make humans liable to be affected by disasters, which are overlapped in urban agglomeration. The five big urban agglomerations of China with strong economic power are the important engines for national economic and social development. However, being in the sea-land mutual interaction belts with a vast hazard-bearing body, they are affected by sea-land compound disasters, and are liable to suffer heavy disaster losses with climate change. It is suggested that government departments concerned should fully recognize the impact of climate change on coastal urban agglomerations, propose strategies as soon as possible, and integrate the impact of climate change and adaptation countermeasures into the various kinds of social-economic development plans for coastal urban regions.

Surface Regional Heat(Cool) Island Effect and Its Diurnal Differences in Arid and Semiarid Resource-based Urban Agglomerations

With the rapid development of urban agglomerations in northwest arid and semiarid regions of China, the scope of the urban heat island(UHI) effect has gradually expanded and gradually connected, and has formed a regional heat island(RHI) with a larger range of impact to the regional environment. However, there are few studies on the heat island effect of urban agglomerations in arid and semiarid regions, so this paper selects the urban agglomeration of Hohhot, Baotou and Ordos(HBO) of Inner Mongolia, China as the study area. Based on the 8-day composite Moderate-resolution Imaging Spectroradiometer(MODIS) surface temperature data(156scenes in all) and land use maps for 2005, 2010, and 2015, we analyze the spatiotemporal distributions of regional heat(cool) islands(RH(C)I) and the responses of surface temperatures to land-use changes in the diurnal and interannual surface cities. The results showed that: 1) from 2005 to 2015, urban areas showed the cold island effect during the day, with the area of the cold island showing a shrinking feature;at night, they showed the heat island effect, with the area of the heat island showing a first decrease and then an increase.2) From 2005 to 2015, the land development(unutilized land to building land) brings the greatest temperature increase(ΔT = 1.36°C)during the day, while the greatest temperature change at night corresponds to the conversion of cultivated land to building land(ΔT =0.78°C) exhibited the largest changes at night. From 2010 to 2015, the land development(grassland to building land) bring the greatest temperature increase(ΔT = 0.85°C) during the day, while the great temperature change at night corresponds to the conversion of water areas to building land(ΔT = 1.38°C) exhibited the largest changes at night. Exploring the spatial and temporal evolution of surface urban heat(cool) islands in urban agglomerations in arid and semiarid regions will help to understand the urbanization characteristics of urban agglomerations and provide a reference for the formulation of policies for the coordinated and healthy development of the region and co-governance of regional environmental problems.

Assessing the impact of manufacturing agglomeration on environmental pollution in Beijing-Tianjin-Hebei region using spatial panel data model

The Beijing-Tianjin-Hebei region is the vanguard of economic development in northern China.Its manufacturing industry is more and more developed,but environmental pollution is also more serious.Based on the data of 13 cities in Beijing-Tianjin-Hebei region from 2017 to 2021,the paper verifies the impact of manufacturing agglomeration on environmental pollution.Both manufacturing agglomeration and environmental pollution are dependent on spatial distribution.Therefore,the paper selects spatial econometric model to study.First,the spatial lag model and spatial error model are constructed,and then the spatial lag model is selected through the results of OLS regression,LM Test and Hausman test,and the empirical process is carried out.Finally,the empirical results are analyzed and the conclusion is drawn.

Urban Agglomeration Formation and Its Spatiotemporal Expansion Process in China: From the Perspective of Industrial Evolution

Urban agglomeration research has received increasing attention in China’s national development strategies, and has become a hot topic in academic research. This study develops a theoretical framework that explores the formation mechanism and expansion process of urban agglomerations from the perspective of industrial evolution, and identifies the development issues and their causes by taking Yangtze Delta and Beijing-Tianjin-Hebei urban agglomerations as case studies. In the process of urban agglomeration formation within a free market, as has happened in Yangtze Delta region, the central city develops first, its secondary industry is then transferred to its neighboring cities, and the work division and cooperation with the neighboring cities is gradually established. However, in the 1990 s, aiming to become an international metropolis, Beijing implemented a series of administrative policies to encourage the reduction of the secondary industry and the development of the tertiary industry, before its secondary industry were fully developed and transferred to its neighboring cities. This delayed the integration process and the development of the Beijing-Tianjin-Hebei urban agglomeration. This study builds a good foundation for the construction of the theoretical system’s urban agglomeration study, and provides references for decision making in an urban agglomeration development.

FORMATION MECHANISM AND SPATIAL PATTERN OF URBAN AGGLOMERATION IN CENTRAL JILIN OF CHINA

Urban agglomeration is made up of cities with different sizes to be linked by traffic network in a given area, and it is an inevitable result when urbanization reaches a certain level. Taking urban agglomeration in central Jilin (UACJ) as an example, this article analyzes the formation mechanism and spatial pattern of urban agglomeration in the less-developed area. First, the dynamics of UACJ has been analyzed from the aspects of geographical condition, economic foundation, policy background, and traffic condition. Then the development process is divided into three stages-single city, city group and city cluster. Secondly, the central cities are identified from the aspects of city cen- trality, and the development axes are classified based on economic communication capacity. Finally, the urban agglo- meration is divided into five urban economic regions in order to establish the reasonable distribution of industries.

A Numerical Study of the Urban Intensity Effect on Fog Evolution in the Beijing-Tianjin-Hebei Region

The influence of urban intensity on fog evolution in the Beijing-Tianjin-Hebei (BTH) region (China) is investigated numerically with the the Weather Research and Forecasting (WRF) model coupled with the urban canopy parameterization-building energy model (UCP- BEM) urban physics scheme. The experiments were designed with a focus on the influence of different urban intensities, which are represented by a different fractional coverage of natural land, buildings, and energy consumption inside buildings in an urban environment. The results of this study indicate that urban areas notably influence fog evolution when natural land is reduced to a small fraction (e.g., less than 10%). Developed land changes fog evolution through urban effects. Higher urban intensity (HUI) generally results in warmer temperatures and lower wind speeds throughout the day, while inhibiting morning specific humidity loss and afternoon specific humidity gain because of the HUI effect on surface heat flux, surface roughness, and surface moisture flux. HUI leads to later and weaker liquid water content formation, with a higher liquid water content base, primarily due to its effect on near surface temperatures. This finding implies that HUI may inhibit the conditions for fog formation. In addition, urban areas with equal natural and developed land coverage seem to greatly enhance the upward surface moisture flux, which is attributed to the combination of a relatively large potential evaporation on developed land and an ample moisture supply from natural land. As a result, the specific humidity increases in the afternoon.

Spheres of Urban Influence and Factors in Beijing-Tianjin-Hebei Metropolitan Region Based on Viewpoint of Administrative Division Adjustment

The coordinated development of Beijing, Tianjin and Hebei has been elevated as China's important strategy. And, the priority in considering how to bring the maximum effect of their coordinated development into play is to delineate the spheres of urban influence with regard to the cities in the Beijing-Tianjin-Hebei Metropolitan Region. By building an evaluation index system of urban comprehensive strength, this paper applies the principal component analysis method to determine centrality strength of the cities, and the breakpoint theory and weighted Voronoi diagram to identify the spheres of urban influence in all central cities of the region. Results show that 13 central cities within the region greatly differ in strength, which can be classified into four tiers and that the spheres of urban influence do not have a high goodness of fit with administrative jurisdiction scope. Cities like Beijing, Tianjin, Shijiazhuang and Handan have larger spheres of urban, spheres of urban influence in Tangshan and Qinhuangdao are basically consistent with their administrative jurisdiction scopes, and seven cities including Langfang and Baoding have smaller spheres of urban influence. So according to these cities' comprehensive strength and spheres of influence, the region can be divided into five plates: Beijing, Tianjin, Shijiazhuang, Tangshan and Handan. The major influence factors for inconsistency between spheres of urban influence and spheres of jurisdiction include difference in urban administrative ranking, small number of central cities with weak strength, discrepancy in the number of counties under jurisdiction, unreasonable spheres of jurisdiction and diversity in topographical conditions. In order to solve the imbalance in the spheres of urban influence and those of jurisdiction and better facilitate the coordinated development of the region, it is advised to adjust administrative areas so as to obtain more optimized urban spatial layout and more reasonable urban scale hierarchy system.

Agglomeration Shadows amid China’s Urbanization:From a High-Speed Railway Perspective

Using China’s county-level panel data of 2007-2016,this paper verifies the existence of agglomeration shadows from an infrastructure development perspective.With high-speed railway(HSR)launch as a quasi-natural experiment,we find that the launch of HSR lines was followed by a decrease in GDP per capita of counties along the route by 2.6 percentage points.This conclusion remains valid after a series of robustness tests and the treatment of potential endogeneity problem.Mechanism analysis suggests that such effect is the most significant for counties within a distance of 97 to 195 km to the nearest central city,which is a manifestation of the“agglomeration shadows.”We also uncover that HSR would spur economic growth for counties with favorable endowments.However,HSR also has a significant negative impact on permanent population in counties.When change in permanent population is taken into account,HSR’s negative impact on the countywide economy becomes smaller.Shrinking permanent population in counties after HSR launch is a manifestation of such agglomeration shadows.HSR has facilitated the free flow of population.These findings point to the possibility that HSR may have induced regional economic equilibrium amid agglomeration.

Does urban technological innovation and cooperation promote its green development?Evidence from cities in the Beijing-Tianjin-Hebei urban agglomeration,China

The internal technological innovation(IT)and external technological cooperation(ET)of a city are crucial drivers for its green development(GD).Although previous studies have extensively explored the effect of IT on GD,IT,ET and GD have not been integrated into the same framework to explore their relationship.Using panel data of 13 cities in the Beijing-Tianjin-Hebei urban agglomeration,this study revealed the spatio-temporal evolution of GD and analyzed the effects of IT and ET on GD from the perspective of baseline impact,spatial effect and synergy effect.Empirical results demonstrate that the level of urban GD has upgraded and the difference in GD between cities has been narrowed though it decreases from the middle to both ends.IT significantly promotes the growth of GD while ET has an inverted U-shaped effect on GD.Under the influence of spatial spillover,IT has a U-shaped effect on the GD of neighboring cities while the effect of ET on neighboring GD is not significant.Additionally,the interaction between IT and ET has not been effective,leading to an insignificant synergy effect on GD.These findings will provide reference for taking rational advantage of IT and ET to facilitate urban GD.

What are the underlying causes and dynamics of land use conflicts in metropolitan junction areas?A case study of the central Chengdu–Chongqing region in China

Land use conflicts(LUCs),as a spatial manifestation of the conflicts in the human-land relationships,have a profound impact on regional sustainable development.For China’s metropolitan junction areas(MJAs),the existence of“administrative district economies”has made the issue of LUCs more prominent.Based on a case study of the central Chengdu–Chongqing region,we conducted an exploratory spatial data analysis of the evolutionary process of regional LUCs.Furthermore,structural equation modeling was utilized to analyze the dynamic mechanism of LUCs in MJAs,with a particular emphasis on exploring the influences of administrative boundary.The results showed that from 2010 to 2020,LUCs in the central Chengdu–Chongqing region continued to worsen,and the spatial process conflict and spatial structure conflict indices increased by more than 30.0%.The intensification of LUCs in the central Chengdu–Chongqing region from 2010 to 2020 was mainly the result of the deterioration of conflicts in evaluation units with low conflict levels.LUCs in China’s metropolitan areas generally presented a circular gradient distribution,weakening from the core to the periphery,but there were some strong isolated conflict zones in the outer regions.LUCs in China’s MJAs were the result of interactions among multiple factors,e.g.,natural environment,socio-economic development,policy and institutional processes,and administrative boundary effects.Administrative boundary affected the flow of socio-economic elements,changing the supply-and-demand competition of stakeholders for land resources,consequently exerting an indirect influence on LUCs.This study advances the theory of the dynamic mechanism of LUCs,and provides theoretical support for the governance of these conflicts in transboundary areas.

Driving factors and spatiotemporal effects of environmental stress in urban agglomeration: Evidence from the Beijing-Tianjin-Hebei region of China

Environmental stress is used as an indicator of the overall pressure on regional environmental systems caused by the output of various pollutants as a result of human activities. Based on the pollutant emissions and socioeconomic databases of the counties in Beijing–Tianjin–Hebei region, this paper comprehensively calculates the environmental stress index(ESI) for the urban agglomeration using the entropy weight method(EWM) at the county scale and analyzes the spatiotemporal patterns and the differences among the four types of major functional zones(MFZ) for the period 2012–2016. In addition, the socioeconomic driving forces of environmental stress are quantitatively estimated using the geographically weighted regression(GWR) method based on the STIRPAT model framework. The results show that:(1) The level of environmental stress in the Beijing–Tianjin–Hebei region was significantly alleviated during that time period, with a decrease in ESI of 54.68% by 2016. This decrease was most significant in Beijing, Tangshan, Tianjin, Shijiazhuang, and other central urban areas, as well as the Binhai New Area. The level of environmental stress in counties decreased gradually from the central urban areas to the suburban areas, and the high-level stress counties were eliminated by 2016.(2) The spatial spillover effect of environmental stress increased further at the county scale from 2012 to 2016, and spatial locking and path dependence emerged in the cities of Tangshan and Tianjin.(3) Urbanized zones(development-optimized and development-prioritized zones) were the major areas bearing environmental pollution in the Beijing–Tianjin–Hebei region in that time period. The ESI accounted for 65.98% of the whole region, where there was a need to focus on the prevention and control of environmental pollution.(4) The driving factors of environmental stress at the county scale included population size and the level of economic development. In addition, the technical capacity of environmental waste disposal, the intensity of agricultural production input, the intensity of territorial development, and the level of urbanization also had a certain degree of influence.(5) There was spatial heterogeneity in the effects of the various driving factors on the level of environmental stress. Thus, it was necessary to adopt differentiated environmental governance and reduction countermeasures in respect of emission sources, according to the intensity and spatiotemporal differences in the driving forces in order to improve the accuracy and adaptability of environmental collaborative control in the Beijing–Tianjin–Hebei region.

Analysis of emergy-based metabolic efficiency and environmental pressure on the local coupling and telecoupling between urbanization and the eco-environment in the Beijing-Tianjin-Hebei urban agglomeration

We use emergy-based urban metabolism analysis in this study to investigate the local coupling and telecoupling between urbanization and the eco-environment in the Beijing-Tianjin-Hebei urban agglomeration. Our analysis encompasses the last 35 years spanning the period between 1980 and 2014. In addition, we analyze urban metabolic efficiency and environmental pressure in these couplings. There are three main conclusions of this study. First, we show that the total metabolic emergy value of the Beijing-Tianjin-Hebei urban agglomeration has increased over the last 35 years, and that external elements have replaced internal ones as the leading contributors to urban metabolism in this region. The proportion of metabolic emergy derived from external elements increased from 30.87% in 1980 to 67.43% in 2014. The emergy extroversion ratio has continued to increase over our study period, while the development of this urban agglomeration had become progressively and more heavily reliant on external elements. Second, over the study period, the metabolic emergy intensity of elements of local coupling and telecoupling in the Beijing-Tianjin-Hebei urban agglomeration has declined at an accelerating rate, from 1.15×10^(21) Sej/100 million RMB in1980 to 9.69×10^(19) Sej/100 million RMB in 2014. This reflects a continuous increase in the economic efficiency of this area.Correspondingly, emergy use per capita increased from 7.8×10^(15) Sej/person in 1980 to 5.83×10^(16) Sej/person in 2014, suggesting a gradual rise in the level of social welfare in this urban agglomeration. However, we also observed a consistently elevated environmental loading ratio(ELR) in our analysis in terms of metabolism of local coupling and telecoupling elements. This result indicates that environmental pressure has also increased constantly within the Beijing-Tianjin-Hebei urban agglomeration. Third,our analysis shows that the ELR of metabolic emergy from internal elements increased from 8.30 in 1980 to 43.46 in 2014, while the ratio from external elements increased from 4.15 to 92.03. Thus, we quantitatively investigated the dependency of development within this urban agglomeration on external elements as well as the resultant environmental load. The conclusions of this study provide the basis for quantitative policy-making in the Beijing-Tianjin-Hebei region, optimizing economic structures, improving economic efficiency, controlling environmental pollution, and promoting the coordinated development of this region.

Spatio-temporal evolution and dynamic simulation of the urban resilience of Beijing-Tianjin-Hebei urban agglomeration

The continuous growth of urban agglomerations in China has increased their complexity as well as vulnerability. In this context, urban resilience is critical for the healthy and sustainable development of urban agglomerations. Focusing on the Beijing-Tianjin-Hebei(BTH) urban agglomeration, this study constructs an urban resilience evaluation system based on four subsystems: economy, society, infrastructure, and ecology. It uses the entropy method to measure the urban resilience of the BTH urban agglomeration from 2000 to 2018.Theil index, standard deviation ellipse, and gray prediction model GM(1,1) methods are used to examine the spatio-temporal evolution and dynamic simulation of urban resilience in this urban agglomeration. Our results show that the comprehensive evaluation index for urban resilience in the BTH urban agglomeration followed a steady upward trend from 2000 to 2018,with an average annual growth rate of 6.72%. There are significant differences in each subsystem’s contribution to urban resilience;overall, economic resilience is the main factor affecting urban resilience, with an average annual growth rate of 8.06%. Spatial differences in urban resilience in the BTH urban agglomeration have decreased from 2000 to 2018, showing the typical characteristic of being greater in the central core area and lower in the surrounding non-core areas. The level of urban resilience in the BTH urban agglomeration is forecast to continue increasing over the next ten years. However, there are still considerable differences between the cities. Policy factors will play a positive role in promoting the resilience level. Based on the evaluation results, corresponding policy recommendations are put forwar to provide scientific data support and a theoretical basis for the resilience construction of the BTH urban agglomeration.

Quantitative simulation and verification of upgrade law of sustainable development in Beijing-Tianjin-Hebei urban agglomeration

The natural formation and development of urban agglomerations is a process in which core cities continue to unite their neighboring cities to enhance sustainability for their own sustainable development.The upgrade mechanism of sustainable development urban agglomeration is a nonlinear composite upgrade curve that is a function of time,increasing with the number of cities.In this paper,the sustainable upgrade function curve,upgrade rate,and upgrade speed of urban agglomerations were solved using a geometrical derivation,and the index system for measuring the upgrade capability of sustainable development of urban agglomerations was established.The dynamic change in economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of a Beijing-Tianjin-Hebei urban agglomeration from 2000 to 2015 was measured by technique for order preference by similarity to an ideal solution and a grey correlation method,and a comprehensive,intercity unite strength model and a unite threshold calculation method for urban agglomerations were established.The research shows that the economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of the Beijing-Tianjin-Hebei urban agglomeration all show a wave-like rising trend.The average annual upgrade speeds during 2000-2015 are,respectively,2.4%.1.67%,1.1%,and 1.74%,with the intercity comprehensive unite strength of urban agglomerations maintaining a general increase;but there is a limit to the joint threshold.From 2000 to 2015,as the core city of the Beijing-Tianjin-Hebei urban agglomeration,Beijing,to enhance its sustainable upgrade capability,jointly developed with Tianjin,Langfang,and Baoding before 2000,Tangshan in 2002,Cangzhou in 2009,Zhangjiakou and Shijiazhuang in 2012,and Chengde in 2014.By 2015,the comprehensive unite strength between Beijing and four cities(Handan,Qinhuangdao,Hengshui,and Xingtai) was still lower than the unite threshold of 6.14.These four cities are relatively far from Beijing,and offer no substantial contribution to the sustainable upgrade capability of Beijing.Through multiple fittings of the upgrade curve using the long-term sequence index of the comprehensive sustainable upgrade capability of Beijing(the core city of the Beijing-Tianjin-Hebei urban agglomeration) from 2000 to 2015,it was found that the simulated curve of the comprehensive sustainable upgrade function of the agglomeration was very similar to the curve of the comprehensive sustainable upgrade capability,which indicates that the simulation results are satisfactory.The future comprehensive sustainable upgrade capability of the agglomeration can be analyzed and predicted by the comprehensive sustainable upgrade function model.This study provides quantitative decision-supporting evidence for promoting the coordinated development of the Beijing-TianjinHebei urban agglomeration and provides theoretical guidance and algorithms for determining the number of cities joined with the sustainable development of national urban agglomerations.