1. Introduction
Climate change is one of the biggest challenges faced by humankind, and its impact is becoming increasingly significant [
1,
2]. It can greatly affect the environment, production system, survival and development of humankind [
3,
4,
5], hence typical extreme events and disasters (e.g., storms, droughts, heatwaves, fires, and floods) have become stronger and more frequent [
6]. The 2022 Intergovernmental Panel on Climate Change (IPCC) annual report demonstrates that the world faces unavoidable climate hazards over the next two decades with global warming of 1.5 °C (2.7 °F), and urgent actions are required to deal with increasing risks [
7]. One commonly acceptable solution is to make rapid and deep cuts in greenhouse gas emissions, particularly carbon dioxide (CO
2) [
8].
The majority of countries in the world have been seeking effective ways to reduce CO
2 emissions. According to previous research, China is currently the largest emitter of CO
2, accounting for 31% of global CO
2 emissions in 2020 due to its rapid economic development and urbanization [
9]. To achieve the net-zero or near-zero CO
2 emissions, the Chinese government has launched a long-term mitigation goal, which indicates that China would reach peak emissions by 2030, and achieve carbon neutrality by 2060 [
10]. Motivated by this national strategy, emerging research regarding carbon emissions in China has been paid much attention in various domains. Typical research focuses include the modelling, prediction, trading and policy evaluation of carbon emissions [
11,
12,
13,
14,
15,
16]. The establishment of effective policies to reduce carbon emissions is critical. Nevertheless, the long-term reduction of carbon emissions remains a key policy challenge for China and the world [
17]. To meet the requirements to establish effective policies, specific, precise, and flexible policies must be proposed to different levels of geographical units (e.g., county, city, province, region, and country). Understanding the trends and trajectories of carbon emissions remains challenging in light of uncertainty about world economies and technological breakthroughs [
18]. In this regard, the discovery of potentially important emission patterns must be performed from historical carbon emission data. The discovery of emission patterns plays a significant role in guiding the formulation of specific, precise, and flexible policies and the coordinated control of carbon emissions. Therefore, this paper focuses mainly on discovering important patterns from carbon emission data.
Carbon emission data are usually time series data, and time series can be classified into three types, i.e., univariate time series, bivariate time series, and multivariate time series [
19,
20]. In this paper, we are particularly interested in bivariate time series, because they can provide more abundant information than conventional univariate time series; furthermore, related consumptions (e.g., time) can be saved compared with complex multivariate time series. As a bivariate time series integrates the information of two different attributes into one coordinate system, it can be fully transferred to an attribute trajectory, which was introduced in [
21] as a novel kind of trajectory. On this basis, traditional trajectory mining techniques can thus be adopted to discover desired movement related patterns.
Nowadays trajectory data are ubiquitous, having benefited from the proliferation of location aware techniques such as the global navigation satellite system (GNSS), Bluetooth, radio frequency identification (RFID), and Wi-Fi. The discovery of movement patterns has an important place in the domains of trajectory data mining as these patterns can exhibit the rules of individuals’ movements and their interactions. Typical movement patterns include the flock pattern [
22,
23,
24,
25,
26], convoy pattern [
27,
28,
29], leadership pattern [
30,
31,
32], moving cluster [
33,
34], and crew [
35]. Among these, the flock pattern has been paid much attention and it commonly plays an important role in many application fields. A flock can be informally depicted as “a group of spatially close objects staying together for a specific time duration”. Correspondingly, assuming geographical units are considered as objects and their attributes staying close for a specific time duration, these geographical units can be regarded as forming a flock. This way, the traditional flock existing between moving objects can be extended to geographical flock existing between geographical units. Given the importance of discovering flock patterns in traditional trajectory data and the shortage of flock pattern discoveries from new attribute trajectory data, this paper aims to discover geographical flock patterns from carbon emission data.
To achieve the discovery of geographical flock patterns, we propose a spatiotemporal graph (STG)-based approach. The proposed approach includes three main parts: first, the carbon emission data are transformed to attribute trajectory data; second, the STGs are generated from attribute trajectory data; third, specific types of geographical flock patterns are discovered from STGs. We adopt two criteria (i.e., the high–low attribute values criterion, and the extreme number–duration values criterion) to derive various types of geographical flock patterns. In short, four corresponding but different types of geographical flock patterns can be derived according to each criterion. A case study is conducted to verify the usefulness and applicability of the proposed approach, in which the original province-level CO
2 emission data in China are employed. The geographical flock patterns of CO
2 emissions are discovered at two levels, i.e., the province level and the geographical region level. The findings of this study may provide us with potential suggestions to assist policy making and the coordinated control of carbon emissions. The framework of this study is shown in
Figure 1. According to this framework, important patterns (i.e., the geographical flock patterns in this paper) can be discovered from carbon emission data, and effective policies in reducing CO
2 emissions may thus be formulated with the support of the discovered important patterns.
3. Results and Discussion
The results are presented on two levels: the province level and the geographical region level. As introduced in Definition 6, three essential parameters (i.e., r, m and k) are involved in geographical flock, and different combination of parameter values may lead to different results. Therefore, it is necessary to determine suitable parameter values when discovering geographical flock patterns. An important principle for determining suitable parameter values is that a fit number (i.e., neither too large nor too small) of geographical flocks has to be discovered. This is because, if the number of discovered geographical flocks is too large (or too small), it may provide too much (or insufficient) information, which can lead to corresponding difficulties in interpretation. Based on this, for parameter r, the smaller its value, the better, because a small value indicates that the changes of attributes are in a small fluctuation range; for parameters m and k, larger values are preferred, because large values indicate that the geographical flock patterns that are more meaningful may be discovered. By considering the strategies for selecting potential parameter values mentioned above, we have tested a large number of different combinations of parameter values. Due to space limitations, only the significant geographical flock patterns from our perspective are presented in detail in the following.
3.1. Geographical Flock Patterns on the Province Level
As mentioned in
Section 2.3.3, two criteria are proposed to derive specific types of geographical flock patterns, therefore, the results based on each criterion at the province level will be presented below.
3.1.1. The High–Low Attribute Values
Four representative geographical flocks were discovered based on the criterion of the high–low attribute values under the combination of parameter values for
r = 15,
m = 3,
k = 3,
high_threshold = 70,
low_threshold = 30. The detailed information of the four geographical flocks can be seen in
Table 3. From
Table 3 we can see that, among all the geographical flocks, one belongs to type C and the other three belong to type B, while none were discovered for types A and D. This is reasonable, because it cannot be guaranteed that all types of geographical flock patterns can be discovered simultaneously under the same combination of parameter values.
According to the four geographical flocks, we can see that three groups of provinces had both a high amount and a low growth rate of total CO2 emission during three continuous years (corresponding to type B). Specifically, the three groups and the corresponding continuous years are the provinces of Zhejiang, Hunan and Guangdong from 2012 to 2014, the provinces of Shanxi, Zhejiang and Guangdong from 2013 to 2015, and the provinces of Liaoning, Zhejiang, Hubei and Sichuan from 2014 to 2016. Generally speaking, the provinces in the same geographical flock performed well in controlling the growth rate of total CO2 emission in the corresponding years, which indicates that the measures and policies adopted have been effective. However, in the corresponding years, their total amounts of CO2 emissions were still very high, which demonstrates that more effective measures may be taken to control the total amount of carbon emissions. Secondly, we can see that one group of provinces had both a low amount and a high growth rate of total CO2 emission (corresponding to type C). The specific provinces and the corresponding years are Hainan, Ningxia and Xinjiang from 2002 to 2004. It can be inferred that the three provinces have performed well in controlling the total amount of CO2 emission, but that the effects of controlling the growth rate of total CO2 emissions were not that satisfactory.
To further explore the spatial relations of the provinces in each geographical flock, we visualize each geographical flock on the map by setting a different color. The visualization is shown in
Figure 5, in which each figure corresponds to a geographical flock, and the provinces involved in the same geographical flock are denoted the same color. From
Figure 5, we can see that there appears to be a stronger spatial relation for the provinces in the geographical flock type B (
Figure 5a–c) than type C (
Figure 5d), as the provinces involved in the geographical flock type B (
Figure 5a–c) are relatively close to each other in space, while the provinces involved in the geographical flock type C (
Figure 5d) have a relatively further geographical distance from each other. Additionally, an interesting finding is that the provinces involved in type B (
Figure 5a–c) have generally stronger comprehensive strength than those involved in type C (
Figure 5d). This indicates that the related factors (such as economy, population and industry) of the provinces in the same type of geographical flock pattern may be similar, an obvious difference in the related factors may exist in the provinces involved in different types of geographical flock patterns. However, this still needs further exploration. In summary, the geographical flock patterns discovered based on this criterion reveal several interesting findings, which can be fully considered when conducting inter-provincial collaborations and when making coordinated policies to effectively control the amount and growth rate of carbon emissions.
3.1.2. The Extreme Number–Duration Values
Two significant geographical flocks were discovered based on the criterion of the extreme number–duration values under the combination of parameter values for
r = 10,
m = 5, and
k = 3. The full information of the two geographical flocks is shown in
Table 4, from which we can observe that one belongs to type II and the other belongs to type III. As for types I and IV, none has ever been discovered under this specific combination of parameter values.
The results show that a maximum number of ten provinces have had similar evolution patterns in both the amount and the growth rate of total CO2 emission in a shortest duration of three continuous years. The specific provinces and the corresponding years are Beijing, Shanxi, Zhejiang, Anhui, Jiangxi, Henan, Hubei, Guangxi, Gansu and Xinjiang from 1998 to 2000. This demonstrates that the ten provinces formed a maximum group which had similar CO2 emissions and lasted for three continuous years. This finding would be applicable to meet the needs of detecting the largest number of provinces with similar CO2 emission so that closer inter-provincial cooperation may be carried out. Secondly, a minimum number of five provinces had similar evolution patterns in both the amount and the growth rate of total CO2 emission in a maximum duration of four continuous years. The specific provinces and the corresponding years are Heilongjiang, Zhejiang, Anhui, Hubei and Sichuan from 2014 to 2017. This shows that the five provinces have had a similar evolution pattern of CO2 emission in a maximum duration of four years. Therefore, if one would like to know the provinces which lasted for the longest duration, this finding can provide the ideal answer. In our view, the results can provide useful suggestions to related governmental departments. Furthermore, one can detect the very groups of provinces which have had similar evolution patterns in carbon emissions by adjusting the values of the three parameters to meet his/her specific demands.
The visualization of the two geographical flocks can be seen in
Figure 6, which gives an overview of the spatial relations of the provinces involved in the same geographical flock. From
Figure 6 we can see that
Figure 6a exhibits an overall strong spatial relation for all the involved provinces, and
Figure 6b presents a strong spatial relation for most of the involved provinces. Therefore, we can infer that geographical locations may have strong effects on the potential groups of provinces which can form a specific type of geographical flock, but other factors can also have particular effects on the final formulation of potential geographical flocks. The findings indicate that further and finer explorations may be conducted to gain further insight on why the provinces with relatively weak spatial relations can form particular geographical flocks so that more scientific, precise and flexible policies and/or strategies can be made in the future.
3.2. Geographical Flock Patterns on the Geographical Region Level
The discovered geographical flock patterns based on each criterion on the geographical region level will be presented in detail in the following.
3.2.1. The High–Low Attribute Values
Two significant geographical flocks were discovered under the criterion of the high–low attribute values. The exact information of the two geographical flocks is listed in
Table 5. From
Table 5 we can see that between the two geographical flocks, one belongs to type B and the other belongs to type C, and none have been discovered for types A and D under this specific combination of parameter values (i.e.,
r = 10,
m = 2,
k = 3,
low_threshold = 40,
high_threshold = 60).
The two geographical flocks reveal that one group of geographical regions has had both a high amount and a low growth rate of total CO2 emission during three continuous years (corresponding to type B). The specific geographical regions and corresponding continuous years are Northeast China and Central China from 2015 to 2018. Secondly, one group of geographical regions has had both a low amount and a high growth rate of total CO2 emission (corresponding to type C). The corresponding geographical regions and continuous years are Northeast China and South China from 2005 to 2007. Note that a common geographical region involved in both groups is Northeast China. According to the results, it can be inferred that Northeast China may have taken effective measures in controlling the growth rate of CO2 emissions, as it has been keeping a steady low growth rate in recent years (2015 ~ 2018) while the growth rate was relatively high in years prior to that (2005 ~ 2007). Based on the results, potential suggestions may be provided to related national governmental departments to carry out effective regional cooperation to work out more targeted policies in better controlling carbon emissions.
Figure 7 exhibits the visualization of the two geographical flocks. From
Figure 7 we can see that the geographical regions in geographical flock type B (
Figure 7a) have relatively stronger spatial relations than those in type C (
Figure 7b), which coincides well with the corresponding finding in
Section 3.1.1. This may provide us additional useful clues on how to produce more scientific strategies to better control carbon emissions in the future.
4. Conclusions
Climate change has become one of the greatest global challenges, and one which can greatly affect humankind. A significant solution for mitigating climate change is to reduce the emissions of greenhouse gas, particularly CO2. To better support the establishment of effective policies for reducing CO2, it is crucial to consider specific sorts of important emission patterns that exist between provinces and/or geographical regions. This paper takes geographical flock patterns as the very important kind of emission pattern which deserves further investigation. We propose an STG-based approach to effectively discover geographical flock patterns. The approach mainly includes three steps, i.e., generating attribute trajectories from CO2 emission data, generating STGs from attribute trajectories, and discovering specific types of geographical flock patterns. In general, eight different types of geographical flock patterns are derived based on two different criteria (i.e., the high–low attribute values criterion and the extreme number–duration values criterion). A case study was conducted on two levels, i.e., the province level and the geographical region level, based on CO2 emission data in China. The results of the case study demonstrate that the proposed approach is effective in discovering the different types of geographical flock patterns, and potentially useful suggestions and insights can be provided to related departments to assist in policy making and in the coordinated control of carbon emissions in the future.
Given the importance of investigating the evolution patterns of CO2 emission between different geographical units, we only took the province-level carbon emission data for case studies. Although the results based on the province-level CO2 emission data appear effective, finer results are still needed. Therefore, fine-granularity CO2 emission data (e.g., data at the city-level) can be adopted as new datasets for further studies to obtain more precise insight. In addition, other attributes which are meaningful to carbon emission can be used to generate attribute trajectories so that the insights and findings can be further extended. Furthermore, new criteria can be developed and adopted to derive specific types of geographical flock patterns according to one’s specific desire, according to which new findings might be acquired.