Urban Carbon Metabolism Optimization Based on a Source–Sink–Flow Framework at the Functional Zone Scale

Abstract

Carbon flow tracking and spatial pattern optimization at the scale of urban functional zones are key scientific challenges in achieving carbon neutrality. However, due to the complexity of carbon metabolism processes within urban functional zones, related studies remain limited. To address these scientific challenges, this study, based on the “source–sink–flow” ecosystem services framework, develops an integrated analytical approach at the scale of urban functional zones. The carbon balance is quantified using the CASA model in combination with multi-source data. A network model is employed to trace carbon flow pathways, identify critical nodes and interruption points, and optimize the urban spatial pattern through a low-carbon land use structure model. The research results indicate that the overall carbon balance in Hangzhou exhibits a spatial pattern of “deficit in the center and surplus in the periphery.” The main urban area shows a significant carbon deficit and relatively poor connectivity in the carbon flow network. Carbon sequestration services primarily flow from peripheral areas (such as Fuyang and Yuhang) with green spaces and agricultural functional zones toward high-emission residential–commercial and commercial–public functional zones in the central area. However, due to the interruption of multiple carbon flow paths, the overall carbon flow transmission capacity is significantly constrained. Through spatial optimization, some carbon deficit nodes were successfully converted into carbon surplus nodes, and disrupted carbon flow edges were repaired, particularly in the main urban area, where 369 carbon flow edges were restored, resulting in a significant improvement in the overall transmission efficiency of the carbon flow network. The carbon flow visualization and spatial optimization methods proposed in this paper provide a new perspective for urban carbon metabolism analysis and offer theoretical support for low-carbon city planning practices.

1. Introduction

In the context of ongoing global climate change and carbon neutrality strategies, cities, as major centers of energy consumption and carbon emissions, are facing increasing pressure to reduce carbon emissions [1]. Integrating ecological principles into urban system research provides a new perspective for understanding the flow and transformation of carbon within cities. Ecosystem service flows focus on the transfer process of ecological services from supply areas (sources) to benefit areas (sinks) [2]. The source area refers to the region where the ecosystem provides services, while the use area is where humans acquire and utilize these services [3]. This flow process essentially represents the transfer paths of material and energy flows that are consumed or used by humans within the ecosystem. There is significant spatial heterogeneity in carbon metabolic capacity across different functional zones within the city; high-density, built-up areas exhibit high carbon emission intensity but limited carbon sink capacity, whereas peripheral ecological functional zones have strong carbon absorption capacity but relatively low demand. This spatial mismatch between supply and demand leads to low carbon metabolic efficiency, thereby affecting the overall urban structure and function [4]. Therefore, studying ecosystem service flows not only helps to reveal the complex spatial processes of urban carbon metabolism but also provides theoretical support for optimizing urban spatial configuration and achieving sustainable development goals [5].

Among the various types of ecosystem service flows, carbon sequestration represents a key service provided by urban green spaces [6]. From the perspective of natural processes, carbon sequestration, as an embodiment of ecosystem services, constitutes a direct benefit obtained by humans from natural systems [7]. Therefore, carbon flow can be regarded as the process through which this service moves from the ecological “source” to the societal “sink” [8]. To address the spatial flows of ecosystem services, existing studies have proposed theoretical tools, such as the cascade model, the TEEB framework [9], and the ecosystem service flow and function model [10]. Although these studies have offered a macro-level understanding of carbon flow, they remain insufficient for capturing the detailed spatial transfer of carbon within urban areas from supply regions to demand regions. Consequently, investigating the spatial processes of carbon emission, sequestration, and transfer within cities from the “source-sink-flow” perspective is expected to provide more refined support for the formulation of effective carbon reduction policies.

Based on this understanding, recent studies on carbon services have attempted to reveal intra-urban carbon flow pathways through approaches like carbon metabolism models and carbon flux analysis [11,12,13]. For example, Zhang et al. [14] constructed a carbon metabolism model for Beijing from 1990 to 2008 using GIS technology and empirical coefficients, analyzing the carbon flows among 28 socio-economic sectors, including agriculture, industry, and transportation, thereby providing effective empirical guidance for reducing carbon emissions through urban planning. Current carbon metabolism models focus primarily on socio-economic processes [15,16], with limited attention to the natural processes among different emission entities. They fail to fully account for the differences in the natural attributes of various emitters within the complex urban system, making it difficult to understand the internal circulation of carbon elements within cities. To address this gap, some studies have attempted to integrate carbon service flows with land use types [17,18]. For instance, Xia et al. [19] combined ecological network analysis with a land use simulation model and proposed a spatially explicit network framework to simulate service flow relationships in urban carbon metabolism. However, in practice, a single land use type often carries multiple functions, making it insufficient as a basic unit for studying carbon flows to comprehensively reflect the actual movement of carbon elements in urban activities. In contrast, the introduction of the “source–sink–flow” network framework, through the classification of urban space based on actual functional zones, enables a methodological shift from static accounting to dynamic process simulation. Unlike previous studies that primarily focused on overall carbon flows between different land use types, such as flows from construction land (carbon sources) to forest land (carbon sinks), while often overlooking the role of green spaces and parks within construction land as carbon sinks, this approach captures the intra-type flows and transformations of carbon sequestration services. By employing a functional zone-based classification, the functional roles of each area within the urban carbon metabolism system—whether as a carbon source, sink, or transmission channel—can be more clearly identified. This allows for a more accurate representation of carbon circulation, transformation, and storage within urban areas, while visually revealing its flow directions and pathways. Therefore, integrating the “source–sink–flow” network framework and shifting the research perspective from conventional land use types to urban functional zones, which can more accurately reflect the complexity of urban activities, is considered essential for accurately assessing urban carbon budgets and carbon flows.

In recent years, the spatial distribution characteristics of urban carbon metabolism have increasingly become a research focus. Various spatial estimation models have been constructed using data from remote sensing [20], land use [21], and geospatial data [22] and other sources to reveal the spatial heterogeneity of urban carbon metabolism. However, current research remains largely at the level of static identification and descriptive characterization [23,24], lacking spatial optimization strategies based on carbon metabolism assessment results. This makes it difficult to meet the practical needs of high-carbon cities in emission reduction efforts. By optimizing the spatial structure of high-value carbon metabolism areas, not only can regional carbon reduction potential be explored, but scientific support can also be provided for territorial spatial planning and urban renewal. Therefore, the development of a research framework focused on the spatial pattern optimization of carbon metabolism is of significant theoretical and practical value.

In view of the above research status and challenges, this study develops an integrated analytical framework based on the “source–sink–flow” concept, using urban functional zones as the basic units of analysis to investigate the spatial processes and optimization strategies of intra-urban carbon flows. This framework overcomes the limitations of traditional land use classifications and city-scale carbon accounting by conducting refined analyses at the functional zone level, aiming to comprehensively reveal the complex mechanisms of urban carbon metabolism. Specifically, the study aims to (1) accurately quantify carbon emissions and carbon sequestration capacity within each functional zone based on urban functional zoning and establish a detailed carbon budget inventory; (2) innovatively introduce a network model to explicitly simulate and visualize the spatial flow paths of carbon sequestration services among functional zones, thereby identifying key carbon source areas, carbon sink areas, and weak links within the flow network; and (3) demonstrate how these detailed carbon flow analyses can be utilized to guide and optimize urban spatial configurations, with the goal of enhancing overall urban carbon balance through targeted spatial optimization strategies. This study seeks to fill the gap in macro-level carbon balance research at the intra-urban spatial scale and provide a replicable theoretical and practical reference for other rapidly urbanizing regions.

2. Study Area and Data Sources

2.1. Study Area

The central urban area of Hangzhou (119°43′ E–120°38′ E, 29°57′ N–30°36′ N) is located in the north-central part of Zhejiang Province, China, and it is regarded as a key component of the Yangtze River Delta urban agglomeration (see Figure 1). It mainly consists of Shangcheng District, Gongshu District, Xihu District, Binjiang District, Qiantang District, Xiaoshan District, Fuyang District, Yuhang District, and Linping District, covering a total area of approximately 4857 square kilometers. This region is characterized by a typical subtropical monsoon climate, with an average annual temperature of 17.2 ± 0.5 °C and annual precipitation of 1500 ± 218 mm, exhibiting a clear pattern of synchronized heat and rainfall. The terrain is primarily composed of plains, hills, and low mountains. The Qiantang River winds through the entire area from southwest to northeast and eventually flows into Hangzhou Bay. Significant ecological areas, such as West Lake and Xixi Wetland, endow Hangzhou with a unique natural landscape.

In recent years, Hangzhou has experienced rapid urbanization, accompanied by sustained growth in both population and the economy. By the end of 2023, the permanent resident population had exceeded 10 million, with an urbanization rate reaching 84.2%. The total economic output surpassed CNY 2 trillion, with the value added of core industries in the digital economy accounting for 28.3%. The accelerated urban expansion has resulted in significant changes in land use patterns, with a considerable increase in construction land and a corresponding reduction in agricultural land and natural ecological space. Furthermore, with the rise of the digital economy and technology industries, Hangzhou has become an important hub for e-commerce and internet-based innovation in China. However, the high degree of urbanization has led to numerous ecological and environmental challenges, seriously impacting the quality of urban development and the well-being of residents. As one of China’s first pilot low-carbon cities, conducting low-carbon urban development in Hangzhou is not only a necessity for its own growth but also offers valuable insights for the construction and management of low-carbon cities worldwide.

2.2. Sources of Data

The data used in this study include remote sensing data, meteorological data, and geospatial data, primarily for the calculation of net primary productivity (NPP) in 2023. Specifically, the remote sensing data consist of the MODIS monthly normalized difference vegetation index (NDVI) with a spatial resolution of 250 m, covering the period from January to December 2023. The meteorological data comprise monthly precipitation and average temperature for the same period, both with a spatial resolution of 1 km, obtained from the National Tibetan Plateau Data Center (https://data.tpdc.ac.cn/, accessed on 2 June 2025). Monthly surface solar radiation data are sourced from the TerraClimate dataset, with a spatial resolution of 4.5 km, accessed via the Google Earth Engine (GEE) platform. Land cover data are derived from the 2023 Chinese Land Cover Dataset (CLCD) at 30 m resolution, provided by Wuhan University. All datasets are standardized products officially released by the respective institutions. To ensure spatial consistency, all datasets were projected to a common coordinate system and resampled to a 1 km resolution, using bilinear interpolation for NDVI, temperature, precipitation, and solar radiation and the nearest-neighbor method for CLCD. In addition, all monthly datasets were processed through multitemporal image band stacking and converted into a raster format to facilitate subsequent carbon balance accounting and spatial analysis.

3. Methodology

The research framework of this paper consists of three main parts, and the “source-sink-flow” analysis logic is the main line throughout the entire research process. First, based on previous research data and the CASA model, this study evaluated surface carbon fixation and identified the carbon balance at the scale of urban functional zones, thereby clarifying the spatial patterns of “source” and “sink” areas. Second, using a “source–sink–flow” network model, the flow paths of carbon sequestration ecosystem services were quantitatively traced, and key connections and disruptions within the carbon emission process were identified. Finally, a low-carbon land-use structure optimization model was employed to simulate interventions targeting typical deficit nodes, and spatial layout optimization strategies were proposed to support the reconstruction of carbon flow and the balanced regulation of ecosystem service provision across urban functional zones. The specific flow is shown in Figure 2.

3.1. Functional Zoning and Carbon Emission Accounting

To achieve carbon balance accounting at the scale of urban functional zones, this study adopted urban functional zone carbon emission data from the authors’ previous research [25] as the basis for carbon flow analysis. In the prior study, OSM road network data were first used to divide the study area into land parcels. Then, Gaode POI data were classified and weighted, and kernel density analysis was applied to identify the types of functional zones and produce a functional zoning map. Subsequently, following the IPCC methodology, carbon emissions for 1602 sample functional zones were calculated based on electricity consumption and natural gas usage data, and the results were used as target variables. On this basis, spatial feature variables, such as VIIRS/NPP nighttime light data, land surface temperature (LST), building area, and building height, were extracted to construct a carbon emission prediction model for urban functional zones. Three machine learning methods—Random Forest (RF), Support Vector Regression (SVR), and XGBoost—were employed for model training and comparison. Samples were randomly divided into a training set (60%), a validation set (20%), and a test set (20%) to ensure independence between model training and evaluation. To enhance model robustness, five-fold cross-validation was applied, and hyperparameter tuning was conducted. Model outputs were compared with the official ODIAC product, demonstrating high accuracy and effectively improving emission estimation in areas with insufficient nighttime light data. Due to space limitations, detailed information on model parameter settings, evaluation metrics, and validation results has been systematically presented in the authors’ previous study [25] and is only briefly described herein.

3.2. Carbon Sequestration Accounting for Functional Zones

The urban carbon metabolism process involves both carbon emissions and carbon absorption, with carbon flow resulting from differences in the carbon emission and absorption capacities of functional zone nodes [26]. NPP not only reflects the productivity of vegetation in natural environments but also reveals the carbon sequestration capacity of the land surface [27]. It is thus commonly used to represent the supply capacity of carbon sequestration services [28]. NPP was calculated using the CASA model to estimate the carbon sequestration in each functional zone. The CASA model, based on the principle of light use efficiency and combined with GIS and remote sensing technology, can accurately simulate the NPP levels of surface vegetation. Based on this, the NPP values for each functional zone were calculated using the statistical analysis functions of ArcGIS, and further estimations of their carbon dioxide sequestration were made. The formula for calculating carbon sequestration is as follows:

$$C_{S_i}=NPP\times {\displaystyle \frac{44}{12}}$$

(1)

where $C_{s_i}$ represents the amount of carbon sequestration in the i-th functional zone and the coefficient 44/12 is the molar mass conversion factor used to convert the unit of carbon (C) to carbon dioxide (CO₂).

The CASA model, as proposed by Zhu (2006) [29], represents the variation in monthly primary productivity of vegetation as the product of absorbed photosynthetically active radiation (APAR) and actual light use efficiency ε(x, t), calculated as follows:

$$NPP\left(x,t\right)=APAR\left(x,t\right)\times \epsilon \left(x,t\right)$$

(2)

where NPP represents net primary productivity, APAR(x,t) is the photosynthetically active radiation absorbed by pixel x in month t (MJ·m²), and ε(x,t) is the actual light use efficiency of pixel x in month t (gC·MJ⁻¹). The photosynthetically active radiation absorbed by vegetation is calculated based on total solar radiation and the proportion of solar radiation absorbed by vegetation, as shown in the following equation:

$$APAR\left(x,t\right)=SOL\left(x,t\right)\times FPAR\left(x,t\right)\times 0.5$$

(3)

where SOL(x,t) is the total solar radiation at pixel x in month t (MJ·m²), FPAR(x,t) represents the proportion of photosynthetically active radiation (PAR) absorbed by the vegetation layer, and the constant 0.5 is the fraction of total solar radiation that is utilized by vegetation as photosynthetically active radiation.

To comprehensively assess the carbon metabolism balance and the supply–demand situation of carbon sequestration services in functional zones, two indicators are introduced: net carbon emissions and the carbon sequestration service supply–demand difference. Among them, net carbon emissions are used to measure the carbon balance within individual functional zones. The calculation formula is as follows:

$${NCE}_i=C_{H_i}-C_{S_i}$$

(4)

where $C_{H_i}$ represents the carbon emissions of the functional zone i, and $C_{S_i}$ represents its carbon sequestration. If $NCE$ > 0, the functional zone is a carbon source; if $CE$< 0, it is a carbon sink. The carbon sequestration service supply–demand difference is used to assess whether the carbon sequestration capacity of a functional zone is sufficient to meet its own or the surrounding areas’ carbon emission demands. When the carbon sequestration supply exceeds the demand, the functional zone is in a carbon surplus state; conversely, it is in a carbon deficit state when the supply is less than the demand.

3.3. Construction of the Carbon Sequestration Service Flow Network Model

This study quantitatively traced urban carbon flows from the perspective of the “source–sink–flow” framework of ecosystem services. Carbon sequestration services connect supply and demand areas through atmospheric circulation, and the carbon fixation demand in one area can be supplemented by the surplus supply from other regions [30]. The spatial distribution of carbon deficits and surpluses is primarily influenced by the mismatch between the supply and demand of carbon sequestration services. In this study, a network model was employed to reveal the carbon sequestration service flows in Hangzhou. The specific process is as follows.

Definition of Nodes: In this study, the geometric centroids of each urban functional zone were extracted using ArcGIS 10.8 and defined as the nodes of the carbon sequestration service flow network model. The weight of each node was defined as the ratio between carbon emissions and carbon sequestration within the corresponding urban functional zone [31], as expressed in the following formula:

$$W_i={\displaystyle \frac{O_i}{I_i}}$$

(5)

where $O_i$ represents the carbon emissions of the urban functional zone during a given period and $I_i$ represents the carbon sequestration amount of the same zone. $W_i$ indicates the self-sufficiency rate of carbon sequestration services. When $W_i$< 1, carbon emissions are less than carbon sequestration, and the zone is identified as a surplus node. When $W_i$> 1, the zone is categorized as a deficit node. Different node colors are used to represent the surplus or deficit status and its intensity.

Definition of Edges: A carbon sequestration service flow from one functional zone to another is defined as an edge between nodes. According to the study by Wang et al. (2020) [32], it is assumed that surplus carbon can flow between nodes. If a node is in a surplus state, carbon service flows are assumed to exist between it and its adjacent nodes. If a node is in a deficit state and its carbon sequestration demand is not supplemented by other nodes, it no longer provides surplus carbon flow to its neighbors, resulting in the disconnection of the corresponding edge. Connected edges are represented by black arrows, indicating the presence of carbon sequestration service flow along the path. Areas without arrows indicate a disconnected edge, meaning that no carbon flow exists along that route. It is important to note that carbon flow supplementation, i.e., flow edges, also exists between adjacent surplus nodes. However, due to the large number of nodes in the study area, the carbon flow connections between these nodes were not visualized in this study.

Network Construction: Based on the above definitions of nodes and edges, the carbon sequestration service flow network was visualized using ArcGIS 10.8. The spatial location of each node was determined by its geographic coordinates, while adjacency in carbon flow paths was identified by calculating the Euclidean distance between grid centroids using the “Generate Near Table” tool in ArcGIS 10.8. Two nodes were considered adjacent if the distance between them did not exceed 100 m.

3.4. Spatial Optimization of Carbon Flow Patterns

A linear programming approach was applied to construct an urban low-carbon land use structure optimization model aiming to minimize urban carbon emissions. The decision variables in the model are the combinations of land area allocated to various functional zones. A total of 13 types of functional zones were defined as decision variables in the carbon metabolism spatial pattern optimization model, namely: residential–green space ($X_1$), residential–agriculture ($X_2$), commercial–green space ($X_3$), commercial–agriculture ($X_4$), industrial–green space ($X_5$), industrial–agriculture $\left(X_6\right)$, public–green space ($X_7$), public–agriculture ($X_8$), science and education–green space ($X_9$), green space plazas ($X_{10}$), green space–agriculture ($X_{11}$), agricultural land ($X_{12}$), and mixed-use zones ($X_{13}$). These functional zones possess certain ecological attributes and have significant carbon sink potential through the absorption of atmospheric CO₂ via vegetation photosynthesis and soil carbon storage.

The model parameters were set with reference to key indicators, such as arable land retention, total construction land area, and per capita land use, specified in the Master Plan for Land Use of Hangzhou (2021–2035), covering nine administrative units within the study area. At the same time, in accordance with the policy requirements of “optimizing urban development boundaries” and “promoting multifunctional land use,” upper and lower area limits, as well as proportional constraints, were imposed on urban functional zones with ecological composite attributes based on their land use types and spatial distribution characteristics. In this way, the optimization results of the model were kept consistent with current policies and spatial development orientations.

Optimization strategies for different types of functional zones were guided by the Ecological Restoration Plan for Territorial Space of Zhejiang Province (2021–2035) and the Pilot Program for Realizing the Value of Ecological Products in Zhejiang Province, and they included the following. (1) For carbon deficit nodes, the strategy involved increasing the area of green space or agricultural land within ecological composite functional zones (e.g., residential–green space, residential–agriculture), thereby raising the proportion of ecological land to reduce carbon emission intensity. (2) For carbon surplus nodes, the focus was on enhancing their carbon sink capacity, enabling them to play a greater role in ecological regulation and carbon storage within the urban carbon management system. Specifically, this involved moderately reducing the area of surrounding functional zones lacking ecological attributes (e.g., residential, residential–commercial, commercial–industrial) to expand green space or agricultural functional zones and further strengthen the overall carbon sink capacity. The objective function is expressed as follows:

$${F\left(x\right)}_{min}={\sum }_{i=1}^n{C}_i{X}_i$$

(6a)

$$s.t.AX\left(\le ,=,\ge \right)B$$

(6b)

$$X\ge 0$$

(6c)

In the formula, s.t. denotes the constraints; $X\ge 0$ represents the non-negativity constraint; A is the constraint coefficient matrix; B denotes the resource limitations; $C_i$ is the net carbon emission density of the i-th type of functional zone; $X_i$ is the decision variable representing the area of the i-th functional zone; and ${F\left(x\right)}_{min}$ denotes the total net carbon emissions of the city under the low-carbon optimization model. The formula for net carbon emission density is as follows:

$$C_i={\displaystyle \frac{C_i^{total}}{s_i}}$$

(7)

where $C_i^{total}$ is the total carbon emissions of the ith functional zone, and $S_i$ is the area of the ith functional zone.

4. Results

4.1. Spatial Pattern of Carbon Balance in Functional Zones

The study area is divided into 3861 functional zones based on its six administrative units (see Figure 3). Among these, 7 were identified as single-function zones, 19 as mixed-function zones, and 1 as a comprehensive-function zone. Figure 4a shows that the overall spatial pattern of carbon sequestration capacity in the study area presents a “low in the center, high on the periphery” distribution. High-value areas are mainly located in Fuyang and southern Xiaoshan, with annual carbon sequestration exceeding 17,000 tons, contributing 42.8% of the total carbon storage. These areas are mainly located in green space–agricultural functional zones rich in ecological resources, such as forested and mountainous lands. In contrast, functional zones characterized by residential and commercial uses, such as Gongshu, Shangcheng, and Binjiang, exhibit weaker carbon sequestration capacity, generally below 1500 tons annually, with some areas even falling below 500 tons. Figure 4b illustrates that carbon emissions show a spatial trend of “high in the center, low on the periphery,” gradually decreasing from east to west. In highly developed areas, such as Shangcheng, Binjiang, and Xihu, carbon emissions generally exceed 20,000 tons per year, with residential–commercial and commercial–public functional zones identified as the main carbon sources.

Figure 4c, which integrates the results of carbon sequestration and carbon emissions, reveals the spatial pattern of the carbon budget in the study area and further reflects the supply–demand relationship of carbon sequestration services. Overall, the carbon budget exhibits a decreasing trend in carbon surplus from the southwest to the eastern regions. Carbon surplus zones are mainly located in agricultural land and green space plaza functional zones in Fuyang and southern Xiaoshan, where annual net carbon emissions are negative and the carbon surplus exceeds 20,000 tons. In contrast, high-intensity developed areas, such as Gongshu, Shangcheng, and Binjiang, exhibit significant carbon deficits, with some residential–industrial and residential–commercial functional zones showing annual net carbon emissions exceeding 190,000 tons. Sub-center areas, such as Qiantang and Yuhang, show relatively balanced carbon budgets, with net carbon emissions close to zero compared to the central and peripheral zones.

4.2. Spatial Pattern of Carbon Sequestration Service Flow Network

Based on node information, the carbon sequestration service was visualized as a service flow network using ArcGIS, as shown in Figure 5. A total of 3861 nodes were identified in the study area, each representing either a carbon surplus or carbon deficit status, while 3602 edges indicated the connections and transmission directions of carbon sequestration service flows. The main urban area (Figure 5a) was identified as a region with a severe shortage of carbon sequestration services, where carbon deficit nodes accounted for 90.3% of the total nodes, and numerous interrupted edges were observed in the carbon flow network. Carbon flow transfer paths are relatively limited; carbon sequestration services primarily flow from residential–green space and green space plaza functional zones to residential and commercial functional zones. The flow directions are relatively concentrated, and the intensity is weak. In the western part of Qiantang District (Figure 5c), Linping District (Figure 5e), and the northern part of Xiaoshan District (Figure 5f), a large number of carbon surplus nodes were identified, accounting for 47.4%, 29.9%, and 42.3% of the total number of nodes in each respective district. Among them, the carbon flow transmission intensity from green space plazas and comprehensive functional zones to commercial and industrial functional zones was the highest. Notably, some non-ecological functional zones also exhibited carbon surplus status. However, due to insufficient excess carbon sequestration capacity, the overall carbon flow supply remained inadequate, making it difficult to effectively meet the carbon fixation demand in central urban functional zones. Although 28.8% and 34.2% of nodes in Fuyang District and Yuhang District (Figure 5b,d), respectively, showed carbon deficits, the interregional transmission driven by atmospheric circulation helped maintain carbon flow paths to some extent, preserving the basic connectivity of the carbon sequestration service flow network.

4.3. Spatial Optimization of Urban Functional Zones Under the Low-Carbon Objective

Spatial pattern optimization under the low-carbon development goal resulted in a significant overall improvement in the carbon surplus levels of functional zones across Hangzhou, with the most notable enhancement observed in the main urban area. As shown in Figure 6, the proportion of carbon surplus nodes in composite functional zones, such as residential–green space, commercial–green space, and industrial–green space, increased from 9.7% before optimization to 13.4% after optimization, representing approximately a 1.38-fold growth. In the green space plaza functional zones, some areas that were previously in a carbon deficit state achieved a positive carbon balance, with significantly enhanced carbon sequestration capacity. Meanwhile, the structural connectivity of the carbon flow network was also improved, with 369 peripheral carbon flow links restored, indicating a notable enhancement in transmission performance. However, due to the high intensity of land development in the main urban area and the limited availability of ecological space for carbon sequestration, the overall carbon surplus remains insufficient to fully offset the high level of emission demand, despite some enhancement in carbon sink capacity. Based on the findings above, it is suggested that in areas with a high concentration of carbon-deficit nodes, surplus-node demonstration zones should be established. Functional types with carbon sink potential should be prioritized in the core areas of these deficit clusters, allowing them to develop into carbon-surplus zones capable of providing carbon sequestration services to surrounding areas, thereby alleviating local imbalances.

In the peripheral areas, Qiantang District, Linping District, and Xiaoshan District exhibited varying degrees of carbon deficit mitigation during the spatial pattern optimization process. In particular, carbon flow paths within ecological composite functional zones, such as industrial–green space, industrial–agriculture, and residential–agriculture, were partially restored, enhancing the service flow and external supply capacity of newly formed carbon surplus nodes. Xiaoshan District demonstrated the most prominent restoration effect (see Figure 7a), with the number of carbon flow edges increasing by 24.8% compared to the pre-optimization state. In contrast, the western part of Qiantang District (see Figure 7b) and the eastern part of Linping District (see Figure 7c) experienced relatively limited restoration of carbon flow edges—accounting for only 15.7% and 7.3% of the original edge count, respectively—due to the sparse distribution of green space or agriculture-based composite functional zones. Additionally, Yuhang District (see Figure 7d) and Fuyang District (see Figure 7e) showed continuous improvement in the carbon sequestration capacity of carbon surplus nodes after optimization, with 13.0% and 15.4% of the nodes, respectively, achieving an increase in carbon surplus levels. This was particularly evident in green space plaza and agricultural land functional zones, which provided strong support for regional carbon flow supply services.

5. Discussion

5.1. Advantages of an Analysis Based on the “Source-Sink-Flow” Model

Conventional studies on urban carbon balance have largely focused on total accounting or macro-regional scales, emphasizing quantitative assessments while neglecting the visualization of spatial carbon flows within complex urban ecosystems [33,34]. The network model constructed in this study, based on the “source-sink-flow” framework, not only quantified the carbon budget status (surplus or deficit) of each functional zone node but, more importantly, visually traced the potential flow paths of carbon sequestration services from supply areas (sources) to beneficiary areas (sinks). The identification of “critical nodes” (high-emission or high-carbon-sink points) and “metabolic bottlenecks” (e.g., disconnected edges) provides a foundation for understanding urban carbon cycle efficiency and developing targeted intervention strategies. Compared with conventional methods that use land use types as analytical units [35,36], this study, based on the scale of functional zones and integrated with carbon flow network modeling, conducted optimization simulations to explore feasible strategies for repairing fractured edges and transforming deficit nodes, thereby demonstrating enhanced managerial precision and greater policy adaptability.

To further understand the structural characteristics and applicability of the carbon flow network, a preliminary comparative analysis was conducted with reference to the study by Li et al. [3] on carbon sink service flows in the Guanzhong–Tianshui Economic Zone. Without considering differences in research scale, both cases exhibited an overall pattern in which carbon sink services were continuously supplied from peripheral ecological areas to built-up urban zones. In Hangzhou, carbon-deficit areas were relatively concentrated, mainly located in the densely populated central districts, while the western urban area, Linping, and Qiantang represented typical carbon-surplus zones. Similarly, in the Guanzhong–Tianshui Economic Zone, carbon deficits were also concentrated in core areas with intensive construction land use—particularly the Guanzhong urban agglomeration represented by Xianyang and Xi’an, as well as the northern plains—characterized by high carbon consumption and strong demand for ecosystem services. In contrast, the surrounding hilly and forest-covered regions of Tianshui formed a relatively continuous carbon-surplus ring that supported the central areas with carbon sink services.

However, in terms of network structure, the use of block-scale functional zoning in this study resulted in a highly fragmented spatial pattern. Combined with the high development intensity in the main urban area, carbon flow paths were more prone to fragmentation, short-range multi-source flows, and dispersed connections, leading to weaker overall connectivity. In contrast, the Guanzhong–Tianshui Economic Zone exhibited stronger network continuity and directional flow. Despite these morphological differences, both cases demonstrated the strong adaptability of the “source–sink–flow” framework in capturing urban carbon flow patterns, particularly in identifying local metabolic barriers and pathway disruptions. This supports the development of differentiated carbon flow optimization strategies tailored to different types of cities.

5.2. Spatial Optimization of Carbon Sequestration Service Allocation

This study adopted a bottom–up approach to optimizing carbon flow pathways, overcoming the limitations of traditional research that often remained confined to static assessments of carbon metabolism outcomes. By establishing a complete chain of “identification–diagnosis–intervention,” it offers a more actionable planning tool for urban carbon governance and provides policymakers with practical strategies for spatial optimization. By identifying core carbon-deficit areas, clarifying intervention priorities, and proposing targeted transformation strategies for composite functional zones, this approach supports urban managers in enhancing carbon sink capacity while maintaining functional compatibility within limited space, thereby enabling more refined and differentiated spatial planning and carbon regulation policy design.

The findings reveal that carbon deficit nodes are primarily concentrated in high-density developed areas, which serve as “pressure points” and metabolic bottlenecks in the urban carbon flow system. Functional transformation of these areas not only helps alleviate local carbon imbalances but also significantly enhances the internal self-regulation capacity of the system, reducing reliance on peripheral ecological spaces and promoting a more balanced and sustainable urban carbon balance. Moreover, composite functional zones involving green space and agriculture demonstrate strong carbon sink capacities and high spatial compatibility. These zones can deliver stable carbon sequestration services while maintaining core urban functions, thus forming an “embedded carbon sink” system. Based on the optimization practices for composite zones, such as residential–green space and commercial–green space in this study, targeted spatial transformation strategies can be proposed for key carbon deficit areas in Hangzhou, such as Shangcheng, Gongshu, and Binjiang, by selecting suitable types of composite functional zones.

Although the optimization strategies proposed in this study were designed to be implemented without altering the original functional attributes of urban zones—thus exhibiting strong practical adaptability—they may still face real-world constraints in high-density built-up areas, such as limited spatial availability and challenges in interest coordination. In particular, the expansion of green spaces may conflict with residential density or land-use efficiency. Future research will further explore the feasibility and multi-objective trade-offs associated with such interventions.

5.3. Limitations and Future Work

The methodology proposed in this study provides theoretical support for optimizing urban carbon metabolism and spatial planning, offering strong practical value—particularly for carbon management practices in rapidly urbanizing areas. However, certain limitations remain. In estimating carbon sink supply, NPP was adopted as the core indicator due to its high temporal resolution, broad spatial coverage, and suitability for inter-regional comparisons. Nevertheless, NPP does not include belowground carbon sinks, such as soil carbon pools, nor does it adequately reflect the differences in sequestration capacity of green spaces caused by variations in plant species and maintenance practices, which may lead to an underestimation of carbon sink potential in some areas. Previous studies have indicated that soil organic carbon exhibits long-term stability, with turnover processes typically spanning decades to centuries [37]. In view of the long-term characteristics of soil carbon stocks and the lack of high-quality monitoring data, such a simplification is considered reasonable at the current stage. Future studies could incorporate high-resolution vegetation classification data and soil carbon flux observations to improve the accuracy of carbon balance estimations.

In addition, the carbon flow simulation did not incorporate intra-urban spatial resistance factors, such as surface continuity, wind field distribution, and anthropogenic disturbances, which may have led to an overestimation of pathway connectivity. Ma and Tian [38] noted that in areas with dominant wind directions or complex terrain, carbon flows often exhibit pronounced spatial directionality, with pathways not strictly following adjacency principles but instead tending to diffuse along prevailing wind corridors or low-resistance channels. Although the dominant wind directions of Hangzhou were considered in the preliminary analysis of this study, an adjacency-based flow setting with equal weighting and without directional constraints was adopted in the simulation to more robustly reflect overall connectivity potential given the atmospheric diffusion effects of carbon flow services at the block scale. Nevertheless, future studies could integrate wind direction, topography, and land cover continuity into urban resistance modeling. In addition, sensitivity analysis and error propagation methods may be applied to evaluate the impacts of data uncertainty on carbon flow structures and spatial optimization outcomes, thereby enhancing the reliability of carbon source and sink calculations.

6. Conclusions

This study, based on the scale of urban functional zones and incorporating the spatial characteristics of carbon sources and sinks, constructed a carbon sequestration service flow network and optimized the spatial configuration of functional zones with the goal of developing a low-carbon city. The main conclusions are as follows:

(1) The carbon balance in Hangzhou exhibits significant spatial variation, characterized by a pattern of “carbon deficit in the center and carbon surplus in the periphery.” The residential–commercial and commercial–public functional zones in the main urban area show high carbon emission intensity and low carbon sequestration capacity, forming evident carbon-deficit areas. In contrast, green space–agricultural functional zones, such as those in Fuyang and southern Xiaoshan, demonstrate strong carbon sequestration capacity and constitute the main carbon sink regions.

(2) The carbon sequestration service flow network reveals the spatial structure of carbon surplus and deficit across different urban areas. Although peripheral areas, such as Fuyang and Yuhang possess strong carbon sink capacity, the total surplus is insufficient, and the high emission intensity in the main urban area leads to numerous disruptions in the central part of the carbon flow network, limiting the efficiency of carbon transmission.

(3) The spatial optimization results show that by adjusting the types and proportions of functional zones—especially by increasing ecologically composite carbon sink areas—the carbon surplus level in the main urban area has improved. Some original carbon-deficit nodes have been transformed into carbon-surplus nodes, and the overall connectivity of the carbon flow network has been enhanced.

In general, the method proposed in this study provides theoretical support for urban carbon metabolism optimization and spatial planning, with good practical applicability, particularly for carbon management in rapidly urbanizing areas. However, the treatment of data completeness and spatial resistance factors in carbon sink estimation and carbon flow modeling remains relatively simplified, and the related methods require further improvement. In addition, the current optimization strategies are based solely on the existing spatial layout and have not been systematically compared with other spatial adjustment approaches or multi-scenario schemes. Future research should incorporate multi-scenario simulations and evaluation mechanisms to more comprehensively identify optimal directions and implementation pathways for spatial optimization.