Urban Expansion Simulation for the Low-Carbon Goal: A Focus on Urban Form Optimization

Abstract

Urbanization significantly reshapes urban form, affecting the spatial and quantitative dynamics of urban land use under carbon constraints. However, the role of macro-scale urban form in guiding low-carbon urban expansion remains underexplored. Our study introduces an integrated Cellular Automata (CA) model to simulate urban land use patterns with regard to the low-carbon goal, focusing on urban form optimization. The model employs a top-down strategy to adjust future urban land demand by balancing urban development needs with carbon emission (CE) reduction targets. The adjusted demand is then used to optimize urban form parameters (i.e., the inverse S-shaped function) to predict future urban land patterns and allocate land increments within concentric rings. Subsequently, a bottom-up strategy incorporating carbon sequestration (CS) conservation is applied to refine urban land conversion. The CA model integrates a maximum probability transformation rule to allocate urban land efficiently. We used the model to simulate urban land use patterns under four scenarios (i.e., Low-carbon Urban Development Scenario (L-UDS), Top-up Urban Development Scenario (T-UDS), Bottom-up Urban Development Scenario (B-UDS), and inverse S-shaped constraint Urban Development Scenario (S-UDS)) for the Changsha–Zhuzhou–Xiangtan (CZX) urban agglomeration in 2035. Results show that the proposed model effectively reconciles the conflict between rapid urbanization and urban carbon management strategies, as evidenced by a 31.25% reduction in carbon emissions in the L-UDS and T-UDS relative to the S-UDS and B-UDS. Furthermore, urban form constraints promote the development of compact and dense urban structures, advancing sustainable urban development goals. This study not only proposes a simulation model capable of effectively promoting compact urban development at the theoretical level, but its findings also offer actionable policy insights for China to address urban sprawl and actively advance low-carbon urban development.

1. Introduction

Global warming has emerged as a critical issue, posing significant threats to human society and natural ecosystems [1,2]. Rapid urbanization has intensified urban carbon dioxide (CO₂) emissions, further exacerbating global warming [3]. Although cities occupy only 2% of the Earth’s land area, they house 50% of the global population and account for 75% of CO₂ emissions, highlighting their central role in global carbon reduction efforts [4,5,6]. Moreover, urban areas are also central to spatial planning efforts. In this context, China’s national strategy for sustainable development incorporates the “dual carbon” target, which mandates peaking greenhouse gas emissions before 2030 and achieving carbon neutrality by 2060 [7,8,9,10]. This can be achieved by optimizing spatial elements such as urban form, density, and functional layout, while equipping cities with the capacity for self-sustaining evolution to reduce CE [11,12,13,14]. Therefore, optimizing urban spatial layouts is imperative for reducing carbon emissions.

Existing methods for optimizing urban spatial layouts can be categorized into ex post estimation and ex ante interventions [15]. The former involves simulating future land use patterns and estimating associated CE and consumption by applying carbon emission coefficients to each land use type [16,17,18]. This approach helps identify areas for emission reduction or enhancement, thereby supporting the achievement of carbon neutrality targets. The latter focuses on optimizing land use patterns by integrating CE policy planning with local spatial allocation strategies [19,20,21,22]. Specifically, carbon-oriented optimization methods, such as those based on CA and spatial optimization algorithms, have been widely applied at both quantitative structural and spatial layout scales, providing valuable insights for spatial planning [23,24,25].

The spatial configuration of land use in urban environments is a critical determinant of human activity patterns, which in turn significantly influence CE [26,27]. As cities expand and evolve, the distribution of land uses, ranging from residential, commercial, and industrial areas to green spaces, can either facilitate or hinder the implementation of sustainable practices. Existing studies have established a strong correlation between urban form and its environmental impacts, particularly regarding energy consumption and CE [28,29]. Urban form governs the functionality and operational efficiency of cities and plays a pivotal role in resource allocation, including land use and infrastructure, which directly affects CE [30,31]. Research has explored the relationship between urban form and CE from multiple perspectives, employing spatial optimization algorithms to align urban form with carbon reduction goals [32,33,34]. Specifically, existing research primarily examines this relationship from macro- and micro-scale perspectives [35]. At the macro scale, urban form refers to a city or urban region’s overall spatial structure and development patterns. It encompasses the distribution of urban elements across the entire urban area, such as land use types, population density, transportation networks, and green spaces [36]. Macro urban form is often characterized by metrics such as urban sprawl [37,38], compactness [39], polycentricity [40,41], and the spatial arrangement of functional zones [42,43]. The distribution of spatial density within cities also serves as a crucial indicator for assessing the form of urban areas at a macro scale. Compact urban form, characterized by high-density development and a roughly circular spatial configuration, has been demonstrated to reduce CE significantly. In contrast, micro-scale urban form refers to urban areas’ localized spatial patterns and physical characteristics at a fine-grained level of changes and interactions [44]. Previous studies have quantified the relationship between CE and urban form using urban characteristics such as size, compactness, and fragmentation, as well as landscape indicators such as landscape pattern index, patch density, and patch area [45,46,47,48]. While patch-level landscape indices can capture static characteristics of individual patches, they fall short in representing dynamic processes observed in multi-temporal remote sensing data. Despite these advancements, existing research predominantly focuses on micro-scale urban form, leaving a significant gap in understanding the optimization of macro-scale urban form and its impact on CE. Addressing this gap is crucial for developing effective strategies to align urban spatial planning with carbon reduction goals.

The core question of this study is how to establish a quantitative link between macro-scale urban form optimization and carbon emission reduction targets. To address the current research, this study proposed an integrated CA model to optimize urban land patterns in terms of the low-carbon goal, focusing on urban form optimization. We define macro-scale urban form as the spatiotemporal configuration characteristics of urban land density. The objective of CE reduction was integrated into a macro-scale land demand forecast, which was subsequently deduced to an inverse S-shaped function to depict future urban form. The innovation lies in treating carbon emission targets not merely as a “demand,” but as a parametric optimization of the inverse S-shaped function. The inverse S-shaped function provides a standardized framework for characterizing urban expansion. By adjusting parameters α, c, and D, we directly map macro-policy objectives into gradient constraints on spatial form. This “form-driven” optimization logic is difficult to achieve with traditional statistical forecasting methods. We are taking the rapidly developing CZX urban agglomeration as a case study. The proposed model achieved the optimized urban land pattern under a low-carbon perspective. We also compared the other scenarios to verify the model’s performance. Furthermore, we discussed the rationality and applicability of the proposed model, focusing on the macro-scale urban form in optimizing low-carbon urban land patterns. The optimized urban land pattern provides an effective reference for the “dual-carbon” target and sustainable urban management in the CZX urban agglomeration and other regions with similar challenges.

2. Study Area

The CZX urban agglomeration in Hunan Province comprises the interconnected cities of Changsha, Zhuzhou, and Xiangtan, along with their surrounding regions (Figure 1). In 2022, the CZX urban agglomeration accounted for 13.2% of Hunan Province’s land area and 29.6% of its permanent population, contributing 42.7% of total carbon emissions. As a regional economic powerhouse with strategic geographical significance, the CZX urban agglomeration plays a pivotal role in driving low-carbon development initiatives in Hunan Province. Its rapid urbanization and industrialization have intensified land use pressures, necessitating a deeper understanding of how different land allocation and urban layout strategies influence CE. By examining the urban form and their associated carbon impacts, our study aims to provide a scientific foundation for optimizing urban planning and land use policies to achieve low-carbon goals.

3. Methods

The framework for simulating urban expansion with regard to low-carbon goals is illustrated in Figure 2. First, a hierarchy of two low-carbon strategies, CE reduction and CS conservation, was integrated into a CA model to optimize urban land patterns. Second, future CEs were projected by establishing a relationship between the historical Digital Number (DN) values of nighttime light remote sensing data and the total CE, followed by adjusting urban land demand to balance urban development needs with CE reduction targets. Third, the modified land use demand was used to derive a future urban inverse S-shaped function that captures the macro-level characteristics of urban form. Fourth, CS conservation was used to adjust the probability of urban land transition, thereby constraining spatial urban expansion in areas with high CS potential. Finally, an integrated CA model incorporating urban form characteristics was developed to simulate urban land patterns under four scenarios. Compared with traditional CA models, this model not only simulates spatial growth but also actively optimizes urban form to achieve a predefined low-carbon intensity.

Specifically, the S-UDS serves as the baseline scenario, employing the inverse S-shaped function to project future urban form. The B-UDS adopts a bottom-up approach, adjusting the combined probability of urban land change to avoid urban expansion encroaching on the land with high-quality CS. The T-UDS employs a top-down approach by adjusting land use demand to align with carbon reduction targets, thereby constraining urban expansion. The L-UDS combines B-UDS and T-UDS, aiming to balance both carbon emission reduction and CS enhancement in shaping urban land patterns.

3.1. Inverse S-Shaped Function and Its Parameter

Jiao et al. observed that urban land density, defined as the ratio of impervious surface area to the available land (excluding major water bodies) within each concentric ring, exhibits a declining trend from the city center outward. The inverse S-shaped function can effectively fit the trend, and its mathematical formulation is presented as follows [49,50,51]:

$$f_{(r)}={\displaystyle \frac{1-c}{1+e^{a[(\frac{2r}{D})-1]}}}+c$$

(1)

where f is the urban land density, r is the distance to the urban center, and e is Euler’s number. Moreover, the function captures the overall spatial configuration of urban land use and encapsulates key characteristics of urban form through its parameters. Specifically, the parameter α reflects the degree of spatial compactness in urban land distribution; c and D denote the density of developed land in the urban center and the spatial extent of the primary urban zone, respectively.

3.2. CA Model Based on Inverse S-Shaped Function

Our model couples top-down and bottom-up strategies. The top-down process predicts the macro-scale urban land demand. The Markov chain method calculates the total required urban area. The bottom-up process allocates this demand at the micro-scale. We use a Cellular Automata (CA) model for this spatial allocation. The inverse S-shaped function serves as the crucial coupling link. It transforms the total land demand into an urban land density distribution. This function calculates the specific land increment within each concentric ring. The CA model then uses a maximum probability transformation rule. It ranks the development probability of all non-urban cells. The top N cells with the highest probabilities are converted into urban land. This iteration continues continuously. It stops when the cumulative converted area exactly meets the macro-scale demand.

Given that urban land density exhibits an inverse S-shaped distribution, future spatial patterns are anticipated to conform to this characteristic pattern. Consequently, urban expansion can be conceptualized as temporal variations in the inverse S-shaped function, characterized by three key parameters (α, c, and D). These parameters in the original status, representing urban compactness, core density, and spatial extent, respectively, were fitted by nonlinear least squares regression analysis using MATLAB R2019 (a), based on concentric ring data and Formula (1). The main challenge involves predicting future parameter values (α, c, and D) while simultaneously addressing the dual requirements of macro-scale demand forecasting and micro-scale allocation. Thus, an integrated CA model has been developed, incorporating an optimization strategy for predicting the parameters of the inverse S-shaped function and a maximum probability transformation rule for the spatial allocation of newly added urban land demand.

3.2.1. Predicting Inverse S-Shaped Function Parameters

The optimization strategy centers on fitting parameters to a predefined inverse S-shaped function using urban land density data from concentric rings. However, future urban land density is unknown, making this challenging. The parameter fitting problem is reformulated as a nonlinear programming task to address this. Based on the physical meanings of the corresponding parameters of the inverse S-shaped function, four discriminants are derived to analyze changes in urban land density and function parameters during the simulation period. The nonlinear programming can be described as follows [49]:

$$\left\{\begin{array}{c}Min z=|{\displaystyle {\sum }_{i=1}^n(f_{(i)}^{t+1}-f_{(i)}^t)}\times A_i-M|\\ For(i=1:n)(f_{(i)}^{t+1}>f_{(i)}^t)\\ D^{t+1}>D^t\\ C^{t+1}\cong C^t\end{array}\right.$$

(2)

where $f_{\left(i\right)}^t$ denotes the initial urban land density and $f_{\left(i\right)}^{t+1}$ denotes the future projected urban land density in the ist concentric ring. A_i is the area of the i_st concentric ring. M is the predicted urban land demand. n is the number of concentric rings. D^t and D^t+1 are the spatial extent (i.e., urban boundary) of the initial and the future urban land pattern, respectively. C^t and C^t+1 are the urban land densities of the initial and future hinterland built-up areas, respectively.

3.2.2. Allocating Newly Added Urban Land

Given the parameters α^t, c^t, D^t, α^t+1, c^t+1, and D^t+1 of the initial and future urban land patterns, the newly added urban land Ni for concentric ring i is calculated as N_i = ($f_{\left(i\right)}^{t+1}$ − $f_{\left(i\right)}^t$) * A_i. CA determines the probability of urban conversion for each cell within ring i. Additionally, to balance computation and accuracy, 100 iterations were used, converting non-urban cells per iteration based on maximum probability until N_i was achieved.

The CA model calculated grid cell occurrence probabilities (TP_i,t) by combining development potential, neighborhood effects, constraint factors, and random variables, and its equation is as follows [52,53]:

$$T{P}_{i,t}=D_i\times N_{i,t}\times C_i\times R_{i,t}$$

(3)

where D_i is the development potential on cell i, Ni,t is the neighborhood effect, C_i is the restriction factor for cell i, and R_i,t is the random coefficient.

3.3. Constraining Urban Expansion to Meet the Low-Carbon Goal

3.3.1. Balance Urban Land Demand with the CE Reduction Goal

Given the challenges in directly acquiring urban CO₂ emission monitoring data, our study utilizes nighttime light remote sensing data as a proxy to estimate CO₂ emissions in the CZX urban agglomeration [54]. Our study fits the relationship between the nighttime light data and the total CE, and its equation is as follows:

$$\begin{array}{c}C=0.2268\times TDN+7022.8\\ C_n=0.0306\times DN\end{array}$$

(4)

where C is the total amount of CE; TDN is the corrected total value of nighttime lighting data in the CZX urban agglomeration; DN is the value of nighttime lighting in the nth county unit; C_n is the CE in the nth county.

3.3.2. Annual Total NPP Simulation Based on Improved Casa Model

Net primary productivity (NPP) is a fundamental indicator of ecosystem CS capacity, where higher NPP directly enhances carbon storage and supports CS conservation efforts by increasing the net carbon fixed through photosynthesis and reducing atmospheric CO₂ levels. Our study generated a high-precision NPP dataset using an improved CASA model [55], and its equation is as follows:

$$NPP(i,t)=SOL(i,t)\times FPAR(i,t)\times T_1(i,t)\times T_2(i,t)\times W(i,t)\times {\epsilon }_{\max }\times a$$

(5)

where SOL(i,t) is the aggregate solar radiation received by image element i at time t. FPAR (i,t) denotes the percentage of photosynthetic radiation captured by the vegetation layer, contingent upon land use/land cover categories and NDVI indices. T₁(i,t) and T₂(i,t) represent the stress on light use efficiency by low- and high-temperature conditions, respectively. W(i,t) is the water stress impact coefficient. ε_max is the maximum light energy use efficiency under ideal conditions (g CgMJ-1). The coefficient a is set to 0.5, denoting the percentage of vegetation-accessible solar energy against total incident radiation.

3.3.3. Adjusting Future Urban Land Demand from the CE Reduction Goal

CE refers to the release of carbon dioxide and other greenhouse gases, typically measured in CO₂ equivalents, resulting from production and consumption activities. Rapid urbanization, population growth, and increased energy consumption have significantly raised CE, contributing to the greenhouse effect and global climate change. At the macro scale, urban land area is the most direct factor planners control. Given its strong correlation with CE, this relationship is a reasonable and practical choice for our study [15,56]. Thus, our study estimates future urban land demand under carbon emission constraints in three steps. Firstly, potential CEs are calculated using an empirical regression with urban land demand predicted by a Markov chain, reflecting historical trends without emission reduction goals. Secondly, the target CE level is set by reducing potential emissions by 21%, aligning with the carbon emission peaking action in the CZX urban agglomeration. Finally, the target urban land demand is derived from an inverse empirical regression with the target emissions. The relationship between CE and urban built-up areas is expressed through empirical regression, and its equation is as follows:

$$CE=0.0091UL{A}^2-2.1552ULA+299.75$$

(6)

where CE is the total carbon emission (unit: ton), and ULA is the urban land area (unit: km²).

3.3.4. Adjusting Future Urban Land Demand in Terms of the CE Reduction Goal

This study utilizes NPP data to characterize CS values. CS denotes the capacity of vegetated patches to absorb atmospheric carbon into the biosphere, playing a critical role in the biological energy cycle of ecosystems. Urban expansion often degrades natural landscapes, negatively impacting the CS potential of these areas. Sustainable urban development must prioritize protecting land parcels that have high CS capabilities. To address this, the normalized CS of patches is incorporated to adjust the integrated urban transition probability, thereby constraining urban expansion in high-NPP areas [15]:

$$CS{R}_i={\displaystyle \frac{C{S}_{\max }-C{S}_i}{C{S}_{\max }-C{S}_{\min }}}$$

(7)

$$TP\_R_{i,t}=T{P}_{i,t}\times CS{R}_i$$

(8)

where CSR_i is the normalized value of CS of land patch I, with lower values representing higher ecological importance and stronger constraints on urban expansion. TP_R_i,t is the modified probability of patch I to be developed at time t.

4. Results

4.1. Urban Form in CZX Urban Agglomeration

Using the nonlinear least squares method in the MATLAB R2019 (a) platform, the inverse S-shaped function of the urban land use pattern of the CZX urban agglomeration from 2000 to 2020 was fitted, revealing the dynamic characteristics of urban spatial expansion. The fitting parameters α, c, and D, along with the fitting curve, are shown in

Table 1. Parameters of urban land density function in CZX urban agglomeration.

Years	α	c	D	${\mathit{R}}^2$
2000	2.254	0.020	6.89	0.981
2005	2.118	0.023	8.03	0.982
2010	2.221	0.043	11.01	0.983
2015	2.127	0.049	12.29	0.982
2020	2.066	0.058	13.12	0.981

and Figure 3. The parameters c and D represent the initial urban land density in the city center and within the city range (from the city center to the city edge), respectively, which increase with the expansion of the city. The parameter α describes the shape of the urban density curve, with higher α representing a compact form of urban expansion. The urbanization process exhibits greater compactness as α values increase. The α value in the central area of CZX fluctuates around 2.1 throughout the year, decreasing from 2.254 to 2.118 from 2000 to 2005, rising to 2.221 from 2005 to 2010, and gradually decreasing to 2.066 from 2010 to 2020. The fluctuation of parameter α implies that the urban form at the macro level alternates between two expansion modes of dispersion and compactness, while the urban scale of the CZX central area (represented by parameter c) increases year by year, indicating that the gradient of urban land density is not absolutely limited by urban scale. The results indicate that as the distance from the city center increases, the urban land density first shows a trend of slow, then rapid, and finally slow decline, exhibiting significant spatial heterogeneity. Furthermore, between 2005 and 2010, the curve underwent the most significant changes, indicating an accelerated phase of urban spatial expansion. In contrast, milder curve shifts were observed between the periods of 2000–2005 and 2015–2020, indicating a relative decrease in the urban expansion rate.

4.2. Spatial Pattern of NPP

NPP serves as a crucial indicator for assessing ecosystem bio-productivity and CS capacity, playing a pivotal role in the context of low-carbon urban development. Our study used the natural discontinuity method to divide the NPP of the 2020 CZX urban agglomeration into five levels (Figure 4). The results indicate that low-level areas are mainly located near the city center, such as Furong District and Tianxin District. The medium-level areas and sub-low-level areas are distributed successively in the suburbs outside the central urban agglomeration. The sub-high-level areas are mainly located around high-level areas, such as the Yuhu and Lusong Districts. High-level areas are mainly concentrated in the northeastern part of the CZX urban agglomeration, including Changsha County, and in the southern outskirts of cities such as Xiangtan County and Lukou District. This difference in spatial distribution reflects a direct relationship between net primary productivity and ecosystem carbon assimilation efficiency, as regions with higher vegetation productivity naturally support greater carbon dioxide uptake. Given the ecological significance of NPP indicators in measuring CS capacity, priority should be given to areas with strong CS capacity to promote atmospheric CO₂ sequestration.

4.3. S-UDS Simulation

Carbon emissions for the main urban area of CZX from 2013 to 2020 were estimated using nighttime remote sensing light data. The fitting equation between CE and urban construction land area from 2000 to 2020 shows a good consistency between urban expansion and CE (Figure 5). The Markov Chain Model (MCM) was used to predict the amount of urban land in 2035 (1105.41 km²) based on historic urban land change. Using Formula (2) and MATLAB R2019 (a) linear fitting, the parameters of the inverse S-function for urban land patterns in 2035 were predicted (α = 2.13971, c = 0.06197, and D = 15.96877). The driving factors of the development potential include the distance to the city center, key transportation nodes, transportation network, as well as physical characteristics such as slope and DEM using the random forest model. The size of the Moore’s neighborhood was set to 3 × 3. Nature reserves and water bodies were configured as constraint factors. The k of the random function was set 3 (Equation (3)). Figure 6 shows the urban land pattern in the CZX urban agglomeration in 2035. The results show that by 2035, the urban land area will reach 1072.04 km², with total carbon emissions amounting to 8447.64 t⁴. Compared to 2020, the urban land area will increase by 235.44 km², while urban carbon emissions will decrease by 589.48 t⁴. It is expected that the new urban land will mainly be concentrated in Yuelu District (24.02 km²), Wangcheng District (34.61 km²), and Changsha County (52.48 km²). In addition, Lukou District shows the slowest rate of urban land growth (2.54%), while Changsha County shows the fastest (45.19%) (

Table 2. Urban built-up area of districts of CZX urban agglomeration during 2020–2035.

District/County	Areas in 2020 (km2)	Areas in 2035 (km2)	Newly Added Urban Areas (km2)	Growth Rate of Urban Land (%)
Furong	33.91	40.22	6.32	18.63
Tianxin	58.47	72.29	13.82	23.64
Yuelu	92.54	116.57	24.02	25.96
Kaifu	58.06	77.71	19.65	33.85
Yuhua	87.44	103.56	16.12	18.43
Wangcheng	74.36	108.97	34.61	46.55
Changsha	116.14	168.62	52.48	45.19
Hetang	27.83	34.83	7.00	25.16
Lusong	18.77	23.68	4.91	26.19
Shifeng	38.90	44.48	5.58	14.35
Tianyuan	48.92	63.06	14.14	28.91
Lukou	17.83	18.28	0.45	2.54
Yuhu	60.75	72.50	11.75	19.34
Yuetang	60.09	78.28	18.18	30.26
Xiangtan	42.59	48.97	6.38	14.98
Total	836.60	1072.04	235.44	28.14

).

4.4. Comparison of Four Scenarios

Four scenarios of urban expansion in 2035 (i.e., S-UDS, B-UDS, T-DUS, and L-DUS) were compared, as shown in Figure 7. The spatial and temporal patterns of CZX urban expansion in 2035 differ significantly across the four scenarios. In the low-carbon-constrained scenarios (T-UDS and L-UDS), the urban land area is 905.37 km², and the newly added urban land area is only 68.80 km², far lower than the expansion scale in the S-UDS and B-UDS (

Table 3. Urban land area of each scenario in 2035.

District/ County	Areas in 2020 (km2)	S-UDS		B-UDS		T-UDS		L-UDS
		Area (km2)	Growth Rate (%)	Area (km2)	Growth Rate (%)	Area (km2)	Growth Rate (%)	Area (km2)	Growth Rate (%)
Furong	33.91	40.22	18.63	39.99	17.95	35.50	4.71	35.39	4.36
Tianxin	58.47	72.29	23.64	71.75	22.72	60.85	4.07	60.68	3.78
Yuelu	92.54	116.57	25.96	117.83	27.32	97.20	5.03	97.33	5.17
Kaifu	58.06	77.71	33.85	77.16	32.90	60.92	4.92	60.82	4.75
Yuhua	87.44	103.56	18.43	102.98	17.77	91.42	4.55	91.42	4.55
Wangcheng	74.36	108.97	46.55	110.80	49.01	91.89	23.57	92.47	24.36
Changsha	116.14	168.62	45.19	167.91	44.58	139.95	20.51	139.47	20.09
Hetang	27.83	34.83	25.16	34.97	25.65	29.16	4.76	29.12	4.64
Lusong	18.77	23.68	26.19	23.21	23.70	19.45	3.66	19.44	3.58
Shifeng	38.90	44.48	14.35	44.78	15.12	40.19	3.31	40.29	3.57
Tianyuan	48.92	63.06	28.91	63.86	30.54	52.67	7.67	53.00	8.35
Lukou	17.83	18.28	2.54	18.32	2.77	17.85	0.15	17.84	0.09
Yuhu	60.75	72.50	19.34	72.74	19.73	63.18	3.99	63.16	3.96
Yuetang	60.09	78.28	30.26	76.92	27.99	61.72	2.71	61.50	2.34
Xiangtan	42.59	48.97	14.98	48.82	14.61	43.43	1.96	43.45	2.01
Total	836.60	1072.04	28.14	1072.04	28.14	905.37	8.22	905.37	8.22

). Moreover, total carbon emissions reached 5807.71 t⁴, a reduction of 3229.4 t⁴ from 2020. Compared with the S-UDS and B-UDS, the total carbon emissions were reduced by 2639.93 t⁴. This difference indicates that low-carbon strategies can curb urban sprawl by limiting land development intensity and adjusting land demand. From a spatial perspective, the newly added urban land exhibits the characteristics of “global agglomeration and local differentiation” across all four scenarios: mainly concentrated in the core areas of Changsha County, Wangcheng District, and Yuelu District, as well as in other areas in the northern part of the CZX urban agglomeration. These areas have become the preferred choice for urban expansion due to their well-established infrastructure and strong economic vitality. However, Xiangtan County and Lukou District in the south have significantly lower growth rates due to their high ecological sensitivity or weak economic radiation capacity. The constraint effect of low-carbon scenarios varies in different regions. For example, in the S-UDS, Wangcheng District’s growth rate reached 46.55%. However, it decreased to 23.57% and 24.36% in the T-UDS and L-UDS, respectively (Table 3), a decrease of nearly 20%, indicating that the region is particularly affected by low-carbon policy regulation due to its great development potential. In contrast, the growth rate of Lukou District is less than 3% in all four scenarios, reflecting its natural limitations on expansion due to ecological protection or land resource endowment.

In addition, the S-UDS and B-UDS share identical macro-scale urban land demands (

Table 4. Total NPP in non-urban areas under each scenario in 2035.

Scenarios	Preserved Total NPP (104 tC)	NPP Loss vs. 2020 (104 tC)	Loss Rate (%)
2020 base	438.46	-	-
S-UDS	431.04	−7.42	1.69%
B-UDS	431.63	−6.83	1.56%
T-UDS	436.26	−2.20	0.50%
L-UDS	436.51	−1.95	0.45%

). However, the B-UDS incorporates the normalized CS factor to adjust transition probabilities. This adjustment penalizes expansion into high-NPP areas. Our spatial overlay analysis shows that the carbon constraints in the B-UDS reduced total NPP loss by 7.9% compared to the S-UDS. This spatial divergence proves that the model is sensitive to ecological parameters. It successfully guides urban growth away from key carbon sinks even with fixed expansion totals. The L-UDS combines the T-UDS with the B-UDS to balance ecological service functions while controlling city size. In this scenario, the NPP suffered a loss of merely 0.45%. The growth rate of Yuelu District in the L-UDS (5.17%) is slightly higher than that in the T-UDS (5.03%), which may be due to the retention of some high CS plots, leading to a moderate transfer of urban land to other low-ecological-value areas. This dynamic balance reflects the multi-objective collaborative mechanism of the low-carbon strategy, which not only avoids “one size fits all” development restrictions but also enhances the resilience of urban systems through spatial optimization.

Fundamentally, the internal logic of these spatial differences stems from the model’s constraint mechanisms. In the S-UDS, the expansion follows historical trends with a low compactness parameter α, resulting in a fragmented layout. In contrast, the L-UDS uses a dual-constraint logic. First, the model optimizes the inverse S-shaped function by increasing the compactness parameter α, which drives new urban growth to cluster around existing urban centers. Second, the CS conservation factor reduces the transition probability of land with high carbon value. This spatial filter prevents expansion from encroaching on critical ecological areas. Together, these mechanisms ensure that the L-UDS results in a more compact, low-carbon urban form. Overall, low-carbon scenarios not only suppress the growth of total urban land use but also guide the concentration of land resources towards regions with high efficiency and low ecological conflicts through differentiated regulation, providing spatial support for achieving carbon neutrality goals in the CZX urban agglomeration by 2035.

5. Discussion

5.1. Rationality of Urban Expansion Modeling Focusing on Urban Form

Integrating macro urban form into urban expansion modeling aimed at achieving low-carbon objectives is theoretically grounded and practically essential. Urban form, quantified through indicators such as density, compactness, polycentricity, and spatial configuration, profoundly influences energy consumption, transportation demand, land use efficiency, and associated CE. Compact and well-structured urban morphologies are widely acknowledged for their capacity to lower per capita energy use by enhancing accessibility, promoting active transportation modes, and facilitating efficient public transit systems. Incorporating these macro-scale morphological characteristics into urban expansion models is therefore critical for accurately capturing the spatial determinants of CE and for supporting land use planning aligned with low-carbon development goals. The omission of urban form in such models risks neglecting the significant impacts of urban spatial structure on ecological environmental outcomes, potentially undermining efforts to reduce CE and achieve long-term sustainability. Methodological frameworks, including CA, agent-based models, and integrated land use and transport models, can be substantially strengthened through integrating urban form indicators, thereby enabling the evaluation of spatial development strategies in terms of their carbon mitigation potential. Furthermore, considering macro urban form enhances the interpretability and policy relevance of modeling outputs, facilitating the design of spatially explicit planning interventions such as zoning regulations, transit-oriented development, and green infrastructure implementation. These strategies align closely with global sustainability agendas, including the SDGs and national carbon neutrality commitments. Thus, embedding macro urban form into urban expansion modeling offers a robust and policy-relevant approach to guiding low-carbon development pathways and advancing sustainable urban development.

5.2. Trade-Off Analysis Between Urban Expansion and Low-Carbon Goals

From the perspective of spatial evolution mechanisms, the inverse S-shaped function changes the intrinsic logic of urban growth. It shifts the expansion model from disorderly sprawl to gradient-based controlled growth. The model achieves this by adjusting the morphological parameters α, c, and D. Following density-decay principles, it directs new urban land to precisely fill gaps within the core built-up areas and the suburban transition zones. This process reveals the balance between land use efficiency and urban expansion. It also proves that applying macro-density gradients effectively regulates carbon efficiency. Moreover, existing simulations typically prioritize accessibility based on distance. Our model treats NPP as a core ecological constraint that directly influences urban land use patterns. Within this framework, NPP effectively suppresses conversion probabilities in high CS areas, rather than merely minimizing commuting distances. This mechanism successfully protects ecologically sensitive zones. Although this negative feedback may cause slight fragmentation at the micro level, it builds an ecologically friendly spatial layout. This indicates that low-carbon urban expansion does not blindly pursue geometric compactness. Instead, it aims for a functional agglomeration that safeguards CS security. Achieving CE reduction targets strictly limits the total urban land supply. However, overemphasizing spatial compactness can harm urban development. Extreme compactness leads to an irrational contraction of the spatial extent parameter D, compressing the internal urban carrying capacity and risking urban issues such as traffic congestion and heat-island effects. Therefore, the L-UDS seeks an optimal balance between land utilization efficiency and environmental resilience. In planning practice, decision-makers must dynamically calibrate urban form parameters based on the city’s specific developmental stage. This approach ensures a sustainable equilibrium between urban expansion and low-carbon constraints.

5.3. Limitations and Outlook

Our study integrates urban form into low-carbon urban expansion modeling to simulate urban dynamics, with its novelty residing in the theoretical and methodological investigation of macro urban form to enhance model performance and guide spatial planning. Nevertheless, several limitations merit attention. Firstly, the proposed model is not applicable in cities where the urban land density pattern does not follow the inverse S-shaped function. The interpretation of model parameters (such as city radius and compactness) is primarily based on the assumption of outward expansion from a single center. In linear or polycentric cities, applying the monocentric model directly yields inaccurate results. In such cases, the model parameters can only reflect the characteristics of the city’s main area and cannot represent the entire city. Other macro urban form indicators (i.e., the geographic micro-process model and spatiotemporal Gaussian model) can also be incorporated into low-carbon urban expansion modeling to capture the heterogeneity of urban growth processes on carbon reduction emissions. Second, we used nighttime light data to estimate CE and used a linear regression model to predict the trend for 2035. This method has certain limitations. Future changes in energy structure and improvements in lighting efficiency may lead to non-linear effects. Simplifying CE as a static function of total urban land area ignores the reality that specific urban forms (such as polycentricity, road structure, and connectivity) affect per capita carbon intensity. Additionally, a single empirical regression analysis lacks multi-source data validation and in-depth uncertainty analysis. In future research, we will integrate energy consumption statistics and traffic flow records and use machine learning models to improve the accuracy and reliability of CE estimation. Third, we used historical data to calibrate model parameters. We extrapolated these parameters to the 2035 simulation, which has significant limitations. Urban form evolves nonlinearly, and historical rules cannot fully represent future urban dynamics. Moreover, low-carbon policies will strongly influence the expansion process, and historical data cannot capture the constraints they impose. Linear extrapolation of parameters may lead to predictions that deviate from reality. Therefore, the 2035 simulation results should be viewed as a scenario trend. It is not an absolute prediction of the future. Finally, while research on urban sprawl mainly focuses on horizontal expansion, emerging trends, driven by smart growth and urban renewal, are characterized by vertical densification. Future research should adopt three-dimensional urban modeling that incorporates vertical land use differentiation and urban form indicators to better capture the spatial and environmental dynamics of urban carbon emissions.

6. Conclusions

Previous studies have mainly explored the relationship between micro urban form and CE, while neglecting the impact of macro urban form. Our study proposed an integrated CA model to optimize urban land patterns toward a low-carbon goal, focusing on urban form. The objective of CE reduction was integrated into a macro-scale land demand forecast, which was subsequently approximated by an inverse S-shaped function to depict future urban form. Moreover, based on this, the urban land pattern of the CZX urban agglomeration was simulated under four scenarios in 2035. The results show that the spatiotemporal pattern of CZX urban expansion in 2035 differs significantly across the four scenarios. Compared with existing CA-based urban expansion models, this model demonstrates significant advantages in simulating the evolution of urban form, such as improving spatial compactness (with higher α in 2035 than in 2020), reducing form fragmentation, and suppressing disorderly urban expansion. This study not only proposes a simulation model that can effectively promote the compact development of urban form at the theoretical level, but, more importantly, its research results can provide operational policy insights for China to respond to urban sprawl and actively promote low-carbon urban development. On the one hand, employing the inverse S-shaped function can guide urban evolution towards compact forms while integrating NPP carbon sinks to preserve high-carbon-sequestration areas; on the other hand, for low-carbon management, urban land demand can be constrained with carbon peak targets. By coupling top-down carbon emission reduction constraints with bottom-up spatial form optimization, this approach offers dual-dimensional policy recommendations for Chinese cities to address urban sprawl. This study also has some limitations, such as the model’s limited universality, limited applicability, and limited accuracy in measuring the CE of urban land use. It is unsuitable for cities where land density patterns do not follow an inverse S-shaped function. Therefore, in the future, other macro urban form indicators can be included in this model, combined with fine-scale urban land CEs, to improve its applicability. Future research will focus on combining models with more refined urban transportation, environmental, and socioeconomic data to further enhance predictive accuracy and the specificity of policy applications.