Differentiated effects of morphological and functional polycentric urban spatial structure on carbon emissions in China: an empirical analysis from remotely sensed nighttime light approach

ABSTRACT Understanding the relationship between urban development and environmental sustainability to achieve ‘double carbon’ goals in China can be strengthened by evaluating the environmental effect of urban spatial structure (US). However, there have been few studies that consider the differentiated effects of polycentric US (PUS) on carbon emissions from both functional and morphological perspectives simultaneously. Thus, taking China’s 31 provinces as experimental subjects, our study developed a novel framework with remotely sensed nighttime light (NTL) data to quantify morphological PUS (MPUS) and functional PUS (FPUS) from 2000 to 2019. Then, from these two dimensions, differentiated effects of PUS on carbon emissions were further examined. Results indicated that NTL data presented high potential in quantifying MPUS and FPUS. The effect of FPUS on carbon emission-cutting outperformed that of MPUS. In addition, the spillover effect effectively enhanced the decreasing effect of the FPUS on carbon emissions. Our empirical findings can provide guidance for the government in developing strategies for reducing carbon emissions and optimizing USs.


Introduction
Global climate change has made reducing carbon emissions a crucial objective for most countries (Sun, Han, and Li 2020;Wu et al. 2022a;Liu et al. 2022a).China has committed to 'carbon reduction' goals in response to the 'net-zero emissions' goal by 2050 (Pan, Xu, and Huang 2021), which has attracted considerable research attention and become the primary concern in China's environment and development.
In addition to energy-saving and emission-reducing technologies and strategies, polycentric urban spatial structure (PUS) effectively affects carbon emissions (Lee and Lee 2014;Liu et al. 2020).PUS has been elucidated in two dimensions in terms of morphology and function.Morphological PUS (MPUS) refers to the balance in the geographical distribution of centers, while functional PUS (FPUS) emphasizes a multidirectional set of functional linkages between centers.The PUS can promote factor flows and market integration to facilitate technology spilloverknowledge sharing among different cities (Huang, Hong, and Ma 2020); and further optimize allocation efficiency of production factors to implement carbon emission reduction.Veneri (2010) examined the relatedness between PUS and external mobility costs of commuting.Researchers concluded that metropolitan areas with MPUS and FPUS effectively reduced the external mobility costs of commuting.However, some studies argued that PUS was environmentally unsustainable given that dispersedly PUS would increase the motorized transportation demand and thus induce additional carbon emissions.Wang et al. (2022a) revealed PUS failed to achieve emission-cutting but rather promoted carbon emissions in urban agglomerations.Other studies have also indicated a U-shape curve reflecting the PUScarbon emissions link (Chen, Zhang, and Ruan 2021c).Historical studies have drawn controversial conclusions because of the lack of reliable methods and robust testing.On the one hand, the development of PUS morphologically affects carbon emissions by changing landscape patterns.On the other hand, anthropogenic energy consumption is influenced by changes in functional configuration and commuting modes in functionally polycentric processes.Moreover, given the difficulty in quantifying FPUS at large geographical scales and long time-series levels, studies have focused on MPUS (Chen, Zhang, and Ruan 2021c; Chen, Chen, and Song 2021a).Thus, given the controversies in previous studies and the complexity of PUS, it is greatly important to unravel the differentiated effects of morphological and functional PUS on carbon emissions.
Therefore, our study aims to gauge and compare the differentiated effects of MPUS and FPUS on carbon emissions.First, we proposed a framework using 31 provinces in China as experimental subjects for developing MPUS and FPUS indices to characterize PUS using remotely sensed nighttime light (NTL) data.Then, the fixed effect (FE) model constructed with PUS indices evaluated the effect of PUS on carbon emissions from multiple dimensions.Third, the effect of spillover effect in differentiated effects of MPUS and FPUS on carbon emissions was also investigated.The following research questions will be addressed in our study: (1) How can we effectively quantify MPUS and FPUS based on NTL data?(2) What effects do carbon emissions respond on MPUS and FPUS? (3) Does FPUS strengthen the emission-cutting effect through the spillover effect?2. Literature review

PUS definition
Studies have generally focused on different urban attributes, like employment size (Sun, Han, and Li 2020) and population (Burgalassi and Luzzati 2015) when measuring the level of MPUS and emphasizing a balance in material elements of different cities within a region.Thus, MPUS primarily depicts the spatial distribution pattern of material elements (Figure 1(a) -(b)).However, a shift toward network thinking has stressed the importance of cities' positions within the inter-city flows of people, information, and goods.Consequently, joint publications and commuting data often reflected in the external connections among cities for calculating the functionally polycentric index (Li and Phelps 2018;Veneri 2010); hence, FPUS refers to the degree of functional connection or flow relationship among internal units (Figure 1 (c) -(d)).Given that MPUS does not imply FPUS, a sound demarcation is made between the two (Burger, van der Knaap, and Wall 2014).As show in Figure 1, MPUS depicts the geographical distribution pattern of centers' material elements, that is, the 'importance' of individual centers, whereas FPUS requires measuring a range of intangible dimensions such as social interactions, as well as firm and knowledge connections.Different from MPUS which considers the relative uniformity of physical characteristics, FPUS emphasizes the functional connectivity through socioeconomic bonds to connect cities (Zhang and Derudder 2019;Burgalassi 2010b).Note that different geographical scales suggest that the focus must be on distinct policy challenges.Therefore, the spatial scale at which PUS exists must be taken into consideration.The spatial distribution of multiple sub-centers within cities or metropolitan areas is considered by the intra-city PUS (Cai, Huang, and Song 2017).These mesoscale (province or city cluster) and macroscale (country or continent) structures refer to a network system composed of multiple central cities (Liu, Derudder, and Wang 2017).Accordingly, our study will be centered around the above scale.

PUS quantification
Quantifying PUS is the foundation for investigating the effect of PUS on carbon emissions.Spatial and socioeconomic attributes of the MPUS obtained from statistical data, such as gross domestic product (GDP), employment, and population, represent physical characteristics of the individual city in the quantification of MPUS relying on Gini coefficient, Primacy, Pareto exponent, and Hirschman Herfindahl index (HHI) (Brezzi and Veneri 2015; Burgalassi 2010a).However, the measurement of MPUS is limited because of statistical defects, such as slow update time, human error, and particularly the inconsistency of statistical caliber.The FPUS involves the processing of geographically functional connections to form a polycentric urban network that focuses on dynamic relationships and interactions; that is, functional connections among subunits.Besides analyzing the intercity linkages via modeling, traffic flow data from transportation (e.g.airlines, railways, highways, and sea transport), location-based service data originating from social media, smart card or cellphone signal (e.g.microblogging checkin data, Baidu mobility data, online car-hailing data, and mobile phone calls), and abstract information flow (e.g. trade contacts, patent cooperation, and academic papers) can effectively describe interactions among cities (Li and Phelps 2018;Yu et al. 2022;Wang, Sun, and Zhang 2022b;Yue et al. 2019b;Wang et al. 2020;Liu, Derudder, and Wu 2016).However, studies focusing on inter-city interactions at long-time and large geographical scales are limited because of the restricted access to high-quality flow data in China (Huang, Hong, and Ma 2020;Guo, Li, and Han 2020).The emergence of NTL data has provided an alternative to traditional data and quantification of spatial interaction among cities (Zhang and Derudder 2019;Tu et al. 2021).Moreover, NTL data capturing anthropogenic light emissions and monitoring the land surface's real-time status can provide a novel perspective in directly representing the urban horizontal and vertical information (Shi, Wu, and Liu 2021), such as economic activities, population sizes, and other socioeconomic aspects (Wu et al. 2021;Zhao et al. 2022;Shi et al. 2014;Chen et al. 2022), as well as identifying urban connectivity and urban networks (Tu et al. 2021;Wang et al. 2022c).Particularly, Jung, Kang, and Kim (2022) selected a total of 103 U.S. metropolitan statistical areas (MSAs) as objects with NTL to identify urban centers.Meanwhile, Yue et al. (2019a) conducted the morphological and functional measurement of polycentricity in a coherent manner using NTL data; Tselios and Stathakis (2018) explored regional and urban clusters and patterns by employing NTL data and revealed the polycentric hierarchical structure of Europe.Thus, NTL data can conveniently, rapidly, and effectively quantify MPUS and FPUS on a large scale.

Relationships between PUS and carbon emissions
The effect of MPUS/FPUS on carbon emissions remains uncertain.Studies have primarily looked at how the MPUS affects pollution levels and energy efficiency.The findings are categorized as follows: (1) Reduced effect.Polycentric development can achieve regional multipolar development with efficiency and balance and affects the scale of economies as well as mitigate urban problems caused by agglomeration diseconomies (Liu et al. 2022a).Liu et al. (2022b) revealed that MPUS significantly mitigated pollution emission effects.Researchers have confirmed that MPUS could also promote the implementation of green carbon reduction policies in China's prefecture-level cities (Zhu, Tu, and Li 2022;Sun, Han, and Li 2020).Makido, Dhakal, and Yamagata (2012) found that polycentric cities can significantly reduce the per capita residential carbon emissions in 50 Japanese cities. (2) Aggravated effect.Wang et al. (2022) indicated that MPUS failed to realize the emission-cutting effect while promoting emissions in some Chinese urban agglomerations.Other studies have confirmed that MPUS weakened the positive effect of agglomeration economies and was correlated with a large living space, thereby negatively affecting energy efficiency and increasing carbon emissions (Zheng et al. 2011;Yu 2021).Jung, Kang, and Kim (2022) proved more urban centers caused more transportation carbon emissions.Moreover, given that traffic congestion would increase the air pollutant emission, Wang and Debbage (2021) analyzed 98 MSAs in the United States and found that PUS would bring more serious traffic congestion, which was consistent with previous studies that uniquely analyzed environmental performance (Ewing, Pendall, and Chen 2003).(3) Nonlinear effect.Chen, Zhang, and Ruan (2021) concluded that a U curve can depict the MPUS's potential effect on carbon emissions.MPUS could promote industrial cooperation and improve energy efficiency for reducing carbon emissions.Nevertheless, excessive polycentric levels would cause more competition among cities and thus hinder efficient energy consumption.(4) No significant effects.Lo (2016) revealed that the environmental behavior of residents remained unaffected by the polycentric nature of 24 OECD metropolitan areas due to their insignificant effects on driving and energy consumption.An insignificant association between MPUSs and emission levels was demonstrated in Türkiye (Sat 2018).
However, studies on the environmental aspects of FPUS are limited because of the restricted access to flow data.For example, Burgalassi and Luzzati (2015) verified that FPUS was positively associated with cutting transportation emissions.However, few studies compared the effects of MPUS and FPUS on carbon emissions.Although both MPUS and FPUS may exert a certain effect on carbon emissions, FPUS may present a stronger emission effect than MPUS due to spillover effects (Wang, Sun, and Zhang 2022b).Cities within a MPUS are isolated and dominated by closed urban development patterns.These cities can only achieve an agglomeration economy by increasing the spatial agglomeration levels through their own population, employment, and economic size growth.Previous studies claimed agglomeration economies were geographically constrained and without spillover effects outside the agglomeration (Burger and Meijers 2016;Huang, Hong, and Ma 2020).Geographical distances limit the cities' spillover effect and radiation coverage (Figure 1 (a) -(b)); thus, whether or not small-sized cities could share the economic benefits of large-sized cities remains unclear (Tang, Guan, and Dou 2021).Conversely, the FPUS is an open urban development pattern.Linkages in the mono-center are manifested as a one-way flow relationship between the central and peripheral cities.The multidirectional flows happen in the borrowing size process while occurring borrowing size effect demands accessibility and network connectivity as prerequisites (i.e. a network perspective) (Burger and Meijers 2016).Accessibility influences the spillover effect within the polycentric network, and cities with satisfactory accessibility can successfully implement borrowing sizes.Thus, multidirectional connections may realize flow and interaction within the polycentric urban network to strengthen the spillover effect and drive the progress of green cleaning technology, which effectively affects energy efficiency and emission reduction to an extent (Huang, Hong, and Ma 2020).

Study areas and data sources
Experimental subjects in our study were 31 provincial administrative units of China consisting of 22 provinces, 5 autonomous regions, and 4 municipalities (Figure 2).The primary reasons for selecting provinces as geographical units are presented as follows.( 1) Interprovincial administrative boundaries caused by market segmentation can remarkably reduce the intensity of spatial spillover and absorption effects of cities on other provincial cities to protect and promote smalland medium-sized cities in China's provinces.(2) Developing a polycentric network governed by the unified development framework in a province is practical and feasible because provinces differ in industrial policies and urban planning.
Five types of data used in our study were as follows: DMSP-OLS-like data, anthropogenic carbon emission datasets, Baidu mobility data, socioeconomic data, and China's national and provincial administrative boundaries.The detailed descriptions of the above data are provided by Table 1.

Quantifying MPUS
Quantifying MPUS is mainly based on the weight of physical characteristics with four indicators (i.e.Primacy, HHI, Gini coefficient, and Pareto exponent).Specifically, Primacy measures how important the first city is.HHI emphasizes the importance of large cities in the spatial structure of the region and gives them more weight.An unbalanced distribution of cities is measured by the Gini coefficient, which calculates how far a city deviates from its average city distribution.Moreover, the Pareto exponent gives equal weight to all cities in the region, reflecting the overall SS of the province.Thus, Primacy describes the 'relative importance' of the largest, HHI aggregates the squares of the proportion of subunits to the province, Gini coefficient measures the balance of urban importance distribution, and the Pareto exponent measures the slope between city size and its rank.In this study, Primacy, HHI, and Gini coefficient are deformed as inverted Primacy, inverted HHI, and inverted Gini coefficient, respectively, to ensure that their trend changes are similar to that of the Pareto exponent in our study.Therefore, inverted Primacy, inverted HHI, and inverted Gini coefficient are expressed as follows: where US 1 is the unit with the maximum total NTL intensity in the province, TUS is the total NTL intensity in the province, US i is the total NTL intensity of the i th city, US is the average total NTL intensity of all subunits in the province, and n is the number of subunits in the province (Figure 3 (a)).The PUS's level of the province increases as the indicator approaches 1.
Parameter values are estimated by subtracting 0.5 from the rank to correct for small sample bias.To correct for small sample bias, subtract 0.5 from the rank before estimating parameter values.Then, the Pareto exponent was calculated on the basis of ranksize distribution theory as follows: where R i represents the ranks of each city in the province.A large MP4 value corresponds to a balanced importance of cities within the province and enhanced polycentricity of a province.C is the constant.According to the radiation model (Simini et al. 2012), an intra-provincial city p interacts with another city q in calculating the interaction intensity of q to p (II pq ) as follows: II pq = TNL 2 p × TNL q (TNL p + NTNL pq ) × (TNL p + TNL q + NTNL pq ) (5) where TNL p and TNL q are the total NTL intensity of cities p and q, respectively, while indicating the development level of cities, and NTNL pq represents the development level of their neighboring cities.The distance between NTL centers of every two cities (p and q) in the province is used as the radius, a circle is formed with the NTL center of p as the center of the circle, all cities in the coverage area, except p and q, are considered their neighboring cities, and the NTL intensity of neighboring cities accumulates in the calculation of NTNL pq .
II pi , ( 7) where II ip and II pi are the interaction intensity of the i th city in the province to city p and city p to the i th city in the province, respectively.II outp indicates the interaction output intensity.II inp refers to the interaction input intensity; and II p is the total intensity of interaction light index.The light interaction index serves as a proxy for flow between cities given that it presents a directional character; hence, II p can effectively reflect the total intensity of interaction between a city and other cities in the province.Thus, FPUS measures are also quantified in the same way as the four indices in Section 3.2.1,namely, FP1 (inverted Primacy), FP2 (inverted HHI), FP3 (inverted Gini coefficient), and FP4 (Pareto exponent) (Burger and Meijers 2011).
where II 1 is the unit with the maximum total interaction intensity in the province, TII is the total interaction intensity in the province, II i is the total interaction intensity of the i th city, II is the average total interaction intensity of all subunits in the province, and R i represents the ranks of each city in the province.C is the constant.

Estimation strategies
The following benchmark regression model was developed to explore the effect of MPUS or FPUS on carbon emissions: where CE represents carbon emissions; Polycentric_index is the core explanatory variable that represents the MPUS or FPUS index; β 1 is the coefficient that measures the elastic relationship between PUS and carbon emissions; X is a set of related controls, including seven variables; and β 0 is the constant.Table 2 describes the variables in detail.

Descriptive analysis
In Figure 4    carbon emission growth in each five-year plan, carbon emissions perform a stable spatial mode in 2010-2019, with minor growth in each province.

Benchmark regression results
Herein, the two-way FE model was utilized based on the Hausman test shown in Table 3. Table 3 summarizes the baseline results for evaluating MPUS and FPUS on carbon emissions.All MPUS indices exhibited a significantly (p < 0.01) negative correlation with carbon emissions and elasticity coefficients of −0.298, −0.362, −0.250, and −0.044.These findings implied that a 1% increment in MPUS can mitigate 0.044%−0.362%carbon emissions.Although population concentration in central cities improves energy use efficiency, population growth is accompanied by crowding effects like shortage of production factors, which would reduce the marginal efficiency of resources and thus increase carbon emissions.For example, vehicle soot exhaust and inadequate gasoline combustion lead to the increase of air pollutants.The higher pollution from vehicle exhaust emissions during traffic congestion compared with that from exhaust emissions under normal vehicle driving conditions increased carbon emissions (Wang and Debbage 2021).Therefore, polycentric development can effectively achieve regional multipolar development with efficiency and balance in China.The MPUS can effectively reduce agglomeration diseconomies without sacrificing the agglomeration economies' positive externalities, further promote coordinated urban development, and curb the increasing emissions given that the MPUS is a form of decentralization, followed by agglomeration.
Columns ( 5) -(8) present the FPUS indices that passed a confidence level of 99% with estimated coefficients of −0.239, −0.519, −0.460, and −0.086; thus, a 1% increase in FPUS could induce 0.086% −0.519% decrease in carbon emissions.Generally, the absolute coefficient values of the FPUS indices are greater than that of the MPUS indices.These findings indicated that although both MPUS and FPUS exert negative effects on carbon emissions, carbon emission reduction is more sensitive to the FPUS than that of the MPUS.Cities within the province rely on transportation, communication, and other infrastructure networks to form an urban network.Thus, small cities could borrow the neighboring large cities' agglomeration economy and avoid reaching the agglomeration economy threshold to exert the agglomeration effect (Yao and Song 2019).Polycentric urban networks allow cities to share agglomeration effects by borrowing size, which contributes to city-to-city division of labor in the industrial sector and realizes the integration of economic activities and production factors in a large geographic area.Meanwhile, its promotion of market integration and factor flows strongly drives the factor efficiency and reduces carbon emission levels (Meijers, Burger, and Hoogerbrugge 2016).Market integration is conducive to strengthening the inter-regional cooperation and exchange and further promotes emissions reducing and energy conserving technologies among regions.Additionally, accelerating factor flow can break down regional trade barriers, optimize industrial structures, and improve resource utilization efficiency, thereby reducing carbon emissions.
For the control variables, population size would significantly promote the increase in carbon emissions.The large increases in energy and resource consumption with population growth, especially under the background of resource misallocation, would increase carbon emissions when a population exceeds a certain threshold, crowding dominates and adversely impacts energy efficiency (Shi et al. 2019).Urbanization and carbon emissions exhibit a significantly inverse relationship at the 1% level, thereby indicating that an improvement in urban development inhibits carbon emission growth (Zhang et al. 2022).Collectively, urbanization and technological advancement encourage clean production technologies and raise public environmental protection awareness (Zhang et al. 2021).The significantly positive coefficient of ES (ln) demonstrates that carbon emissions increase along with the rapid growth of the economy.In fact, this finding corresponds with the actual state of affairs in China.The rest controls' estimator is consistent with the results of historical studies, and technological innovation and industrial restructuring lead to advanced, new, and clean production and processing methods that can suppress carbon emissions while increasing industrial output; note that electricity demand will promote additional energy consumption and aggravate carbon emissions (Shahbaz et al. 2014).

Robustness analysis
Sample municipality elimination using different measures of carbon emission level and the polycentric index were applied in this section to verify the robustness of the main findings.(1) Sample municipality elimination.The PUS index (MP1-3, FP1-3) of municipalities is set to 0 to represent strong mono-centricity because of the particularity of municipalities.The robustness test results without the interference of municipalities are listed in Table 4. Columns 1-3 show an MPUS that negatively affects the increase of carbon emission with estimates of −0.224, −0.311, and −0.248; meanwhile, the negative signs and significance of FP1, FP2, and FP3 in columns 4-6 are consistent with the baseline results.
(2) Re-evaluation of the carbon emission level as carbon intensity.Herein, we re-measured carbon intensity as the dependent variable and then re-estimated the results in Table 5.In addition, the regression parameters of MPUS/FPUS on carbon intensity are significantly negative, which implies conclusions are similar to our main findings.(3) Replacement of the PUS index.The MPUS index based on HHI was recalculated using the traditional demographic data to explore whether or not the previous empirical partial conclusions remain after  the replacement of the morphological polycentric index.Our study verified the information based on the existing data because of the lack of data in some regions (Tibet, Xinjiang, and Qinghai).When municipalities are excluded or control variables are added or not (Table 6), columns 1 and 4 present that the estimators of the polycentric index are negative with a 1% significant level, thereby supporting the findings.Consequently, these analyses confirmed that the main findings remained valid.The MPUS/FPUS-oriented spatial planning may be an appropriate strategy that can reduce carbon emissions in China, and the FPUS has more effectively improved the efficiency in carbon emission reduction.

Regional heterogeneity analysis
We divided China's provinces into three regions and conducted a regional heterogeneity analysis.Table 7 lists the regional heterogeneity results for MP2/FP2 as an example.In the Eastern region, both MPUS and FPUS significantly negatively affect carbon emissions.This revealed that MPUS and FPUS would reduce carbon emissions.The results also confirmed the previous conclusion that FPUS was more effective in reducing carbon emissions than MPUS.In contrast, neither the Central nor the Western regions showed fully significant results.Interestingly, MPUS positively affects carbon emissions in the Western region.This indicates that agglomeration diseconomy may have far fewer negative externalities in Western regions than its benefits because the Western region lags in industrialization and urbanization.The concentration of economic activities in central cities produces an agglomeration effect to improve energy efficiency and thus realize emissioncutting.Therefore, the agglomeration economy brought about by the monocentric development pattern remained an important driving force for sustainable development in Western China (Chen, Qiu, and Sun 2021b).

Rationality evaluation of PUS quantification based on nighttime light data
Although NTL data are often argued to represent the MPUS, they are rarely proven to represent the FPUS (Yue et al. 2019a;Tu et al. 2021).This section mainly verifies the rationality of FPUS quantification from NTL data.Emerging data sources and traditional data are employed to verify the rationality and accuracy of FPUS from the interaction light index.First, we fitted the interaction light index and Baidu mobility data.Second, because the strength of economic network linkage among cities is reflected in our study when the interaction intensity of the flow was considered, a theoretical model (i.e. the gravity model) was employed to determine the economic relationship among cities with GDP and population, and the economic network linkage is compared with the interaction light index.Interaction light index and Baidu mobility data fitting results in 27 provinces in Figure 6 and Table S1 demonstrated that the interaction light index fits properly with Baidu mobility data and the average r values can reach 0.5 per month.These findings confirmed that the construction of the interaction light index is reasonable and can be applied to investigations on the flow connection among cities.Among the provinces, r values of Sichuan, Hunan, and Ningxia are around 0.9, whereas those of Hebei, Shanxi, Shandong, and Henan are relatively low.This weak correlation is reasonable because urban network interaction involves not only population movement, but also governance, planning control, transportation infrastructure, and environmental characteristics.
Furthermore, we compared economic flows with the interaction light index to validate our findings as population flows are only one aspect of urban network interactions.Our study employed the gravity model with consistent success in explaining economic activity while considering the difficulty in obtaining economic flows to measure economic relations between cities (Pöyhönen 1963;Barthélemy 2011).Meanwhile, Guo, Li, and Han (2020) revealed that the coupling degree between high-speed rail (HSR) and economic flows within three urban agglomerations in China  is above 0.6.The finding confirmed the construction of the economic flows based on the gravity model that effectively characterizes interactions among cities.Therefore, this study refers to the method of Guo, Li, and Han (2020) in calculating economic flows among cities within the province and conducting experiments to compare with the interaction light index.Figure 7 and Table S2 show a strong positive correlation between interaction light index and economic flows.The average r values in Guangdong, Jilin, Ningxia, and other provinces are above 0.9, while those in Jiangsu (0.315) and Hubei (0.310) are relatively low and those in other provinces range from 0.5-0.8(Table S2).Therefore, these results further verify the accuracy of the interaction light index and the rationality of the constructed FPUS index.
Traditionally, statistical data were used to quantify MPUS based on urban attributes such as GDP and population size.However, the lack of digital forms and spatial information, as well as the long lag time between generation and analysis, led to the inability to solve many problems using statistical data (Shi, Wu, and Liu 2021).Lastly, while GDP and population can describe urban attributes, they only provide a partial picture of the information on urban development.
In the case of urban attribute monitoring, NTL data can provide a new perspective, since they can detect even highly inconspicuous lights, including low-intensity lighting from traffic flow and small residential areas (Wu et al. 2022).Therefore, NTL data could indeed portray anthropogenic activities to reflect socioeconomic conditions and actual urban development status, which measures the level of MPUS.
Generally, traffic flow data, location-based service data, and abstract information flow data are subjected to manual statistics, hence, they have the same defects as statistical data.Due to China's policy restrictions, high-precision flow data cannot be freely accessed by the public; however, longtime series interaction data can be obtained through modeling with NTL data.Therefore, analyzing FPUS with NTL data has several advantages.First, compared to the traditional data, the data easy to access and low-in-cost.Especially in areas where reliable statistics are lacking, such as Tibet, it has great potential and application value.Second, NTL data can be used for investigation at various spatial scales as well as compensating for statistical data of inconsistent caliber and incompleteness.Third, NTL data updates quickly, allowing real-time monitoring of urban interaction.Therefore, in local as well as global contexts, quantifying MPUS and FPUS using NTL data can compensate for the shortcomings of traditional data.

Evaluation of the spillover effect
On the basis of the benchmark results, the FPUS outperformed the MPUS in terms of carbon emission reduction.The occurrence of borrowing size remains nearly impossible in the MPUS because cities' radiation coverage and spillover effect are geographically constrained decay with distance.However, FPUS is not spatially confined and relies more on the quality of the functional connections between cities than on their proximity to one another (Huang, Hong, and Ma 2020).Hence, this study mainly investigated whether or not the spillover effect enhances the decreasing effect of FPUS on carbon emissions.
The borrowing size effect would be further exploited with the increasing improvement of transportation.There was further strengthening of the division of labor between large-sized and smallsized cities.Additionally, the FPUS can enhance the spillover effects inside the polycentric network by borrowing size (Yao and Wu 2020).Thus, the borrowing size effect could be regarded as the embodiment of the spillover effect.
We utilized the residual method (Wang, Sun, and Zhang 2022b) to measure the borrowing size and determined whether the spillover effect contributes to emissions reduction on the basis of the FPUS given that specifically quantifying the strength of the spillover effect is impossible.The empirical estimations are listed in Table 8.Estimators of 0.630 (FP1), 1.523 (FP2), and 1.241 (FP3) in columns (1) -(3) exceeded the 99% confidence level (p < 0.01) with positive signs.This finding indicates that the 1% increment in FPUS can positively promote spillover effect rising by 0.630% to 1.523%.In the corresponding empirical results, the spillover effect is significantly negative correlated with carbon emissions (p < 0.01).We introduced an interaction term between the FPUS (Polycentric index) and spillover effects (BOR (ln)) into the basic model.The interaction term detected that the spillover effect moderates the link between FPUS and carbon emissions.The coefficients of interaction term (Polycentric index × BOR (ln)) is significantly positive at the 1% level range from 0.140-0.200with negative signs in columns ( 5) -(7).This suggests that the spillover effect could enhance the decreasing effect of the FPUS on carbon emissions.Opportunities for interactions among cities grow concomitantly due to the increase of spillover effects, thereby boosting the borrowing size effect.
Through polycentric network externalities, FPUS promotes factor flows and market integration to accelerate technology spillovers and knowledge sharing between cities (Huang, Hong, and Ma 2020), which achieves optimization of production factor allocation efficiency to reduce pollutant emissions, especially carbon emissions.In particular, on the one hand, FPUS contributes to realizing the integration of economic activities and factors of production on a larger geographic scale through industrial division between cities by spillover effects, thus, factors efficiency would be strongly promoted to maximize energy efficiency.On the other hand, with the spillover effects in FPUS, cities absorb external knowledge and enhance interaction with local knowledge by establishing a knowledge flow system of Local Buzz and Global Pipeline, thus improving innovation performance and the efficiency of innovation resource allocation.In brief, FPUS is a panacea to reducing carbon emissions because it matches resources on a larger spatial scale and improves the efficiency of production factor allocation (Tang, Guan, and Dou 2021).

Conclusions
Our study used 31 provinces in China as samples to determine the differentiated effects of PUS on carbon emissions from MPUS and FPUS dimensions.The results indicated that using NTL data can not only effectively develop MPUS index, but also quantify the strength of interactions among cities combined with the modified radiation models and thus enable FPUS index calculations.While MPUS and FPUS both contribute to carbon emission reduction, the FPUS has a greater impact on reducing carbon emissions.The spillover effect enhanced the benefits of FPUS in reducing carbon emissions.Generally, our study demonstrated the dominant role of the FPUS in reducing carbon emissions.
The limitations of our study require further exploration in the future.The NTL data (i.e.DMSP-OLS-like data) used in our study suffer from spillover and saturation effects.Hence, the overor underestimation of the urban development level of some cities will affect the accuracy of the calculated intercity interaction.Accordingly, we will attempt to combine additional refined multisource data to optimize the quantification of intercity interactions in the future.We need to perform an indepth exploration of the effects of MPUS and FPUS on carbon emissions at multiscale levels and then compare the differentiated effects between various scales given that the MPUS/FPUS is highly correlated with the geographic scale.Furthermore, in terms of planning practices, our empirical results are relatively straightforward and can provide insight into the overall relationship between PUS and carbon emissions.Based on the China's case study, the tested and confirmed research hypotheses may provide useful information for regional policymakers and the conclusions may have broad implications.The focus on morphological polycentric development may even lead to unsustainable regional development.It is imperative that regional planning and development policies refocus on promoting functional polycentric networks.First, a polycentric network can be achieved by enhancing interprovincial transportation and increasing factor flow between cities.Second, the central city transfers production factors to the nearby small and medium-sized cities, thereby resulting in a polycentric network pattern with coordinated development of the large and medium-sized cities.Third, the polycentric network can avoid excessive concentrations of population and economic activities, which protects the region's ecological pattern and facilitates the development of new ones.
3.2.2.Quantifying FPUS This study utilized the modified radiation model based on NTL data for measuring urban interaction intensity within a province and the attractiveness of each city prior to the measurement of FPUS (Tu et al. 2021) (Figure 3(b)).

Figure 3 .
Figure 3. (a) Spatial distribution pattern of material elements; (b) Scenarios for the interaction intensity (II pq ) from the city p to the city q.
, the PUS distribution of China's provinces has evolved from 2000 to 2019 based on the Pareto exponent (MP4 and FP4).The MPUS of provinces in China from 2000 to 2019 shows a polycentralized trend from the Eastern to the Western region (Figure 4(a) -(c)).Since 2000, it has been the government's policy to coordinate the development of different cities, while the population

Figure 6 .
Figure 6.Pearson correlations between Baidu mobility data from January to December 2020 and the interaction light index of cities within provinces in 2019.

Figure 7 .
Figure 7. Pearson correlation between the interaction light index and urban economic flow constructed on the basis of the gravity model.

Table 1 .
Descriptions and sources of data used in this study.
(Change 2007) carbon emissions data (1-km) were acquired from the ODIAC fossil fuel emission dataset(Change 2007).ODIAC fossil fuel emission dataset refers to the grid data of carbon emissions from fossil fuel combustion, cement production, and gas flaring.The data can locate users' behavior trajectories using hundreds of millions of mobile phones and apps.It has the advantages of high-precision positioning data, thereby covering all modes of transportation and a wide range of users, and can also clearly reflect the urban network in China.https://dataverse.harvard.edu/dataset.xhtml?persistentId=10.7910/DVN/FAEZIO

Table 3 .
Baseline results of the two-way fixed effect estimates.

Table 4 .
Robustness tests with excluding sample municipalities.

Table 5 .
Robustness tests with the substitution of core explanatory variables as carbon intensity.

Table 6 .
Robustness tests with the replacement of core explanatory variable.

Table 8 .
The spillover effect assessment.