From a systematic geographical perspective, the land surface is composed of natural complexes that integrate the characteristics of multiple eco-geographical elements, including geomorphology, climate, vegetation, and soil. Geographers have long sought a universal law of spatial differentiation that can systematize the complexity of these eco-geographical elements (von Humboldt, 1817; Köppen, 1936; Bailey, 1983; Zheng, 2008; Fu et al., 2013). Various conceptual schemes have been proposed for the regionalization of land surfaces, such as Humboldt’s Isothermen (Humboldt, 1817), Köppen’s climate classification (Köppen, 1936), integrated physical regionalization (Huang, 1989), eco-geographical regionalization (Zheng, 2008), and ecological regionalization (Fu et al., 2013). These schemes consider both the spatially ordered distribution and temporal dynamic equilibrium of natural complexes. The regional boundaries of these complexes can be delineated hierarchically based on the principles of systematization, dominance, and relative consistency, with reference also to administrative boundaries (Zheng, 2008; Wu et al., 2016). Such a study is termed ‘regionalization’. Regionalization can contribute to a better understanding of the spatial differentiation of resources and ecosystems, and therefore, may be used to guide agricultural production and ecological management. In addition, with the help of regionalization map, the study results of geography could be better showed and clarified (Mao et al., 2014; Gao et al., 2016; Yin et al., 2019a).

Regionalization is based on a geographical point of view, with the land surface as the object, and can reveal how regions can be differentiated from each other (Huang, 1959; Zheng, 2008). Regionalization provides a representation of geographical units and the spatio-temporal relationships between them, and utilizes existing data and knowledge as part of the process. From the mid-20th century, national construction developed rapidly in China to provide a scientific reference for national development (Wu et al., 2016). Until now, the traditional regionalization studies have been based mainly on the quantitative gradation of natural indices. However, after the gradation of indicator, in the step of synthesizing multiple indicators for comprehensively delineating boundaries, geographers currently have to rely on research or experience to judge the delineation, owing to the lack of a common approach. Therefore, decisions regarding the delineation need to be discussed at length before they can be made, and require the decision-making experts to have a deep knowledge of geography (Peng et al., 2018). In addition, the results of regionalization have generally been dependent on experts and non-repeatable, even using the same methodology (Niesterowicz et al., 2016; Wu et al., 2017). To carry out quantitative comparative analysis of regional boundaries for different periods, a quantitative regionalization method needs to be developed.

Increasingly significant environmental changes at the global and continental scales also require further development of regionalization research. During the past century, climate change has brought about substantial impacts on natural systems (IPCC, 2013). Changes in the distribution of heat and water have resulted in the altered evolution of natural zones on the land surface (Mahlstein et al., 2013). During the second half of the 20th century, the global terrestrial surface system generally became warmer and dryer, showing a trend of polar-ward movement of climatic zones (Chan and Wu, 2015; Spinoni et al., 2015b). At the same time, the world’s arid regions are transitioning to drier types (Huang et al., 2016). The above shifts in natural zones show the significant impact of climate change on the distribution and pattern of natural elements. However, the distribution of temperature zones or humidity regions represents a statistical classification of single indicators. Therefore, the same temperature zone or humidity region may be composed of multiple scattered small areas, and the boundaries between different zones or regions are generally rough and unclear. In addition, research on changes in the boundaries or areas of natural zones (e.g., the cold temperate zone) is more like a study on changes in the distribution of elements with a certain range of values (e.g., a thermal growing season of < 100 d). The development of a quantitative regionalization method could help to further understand the spatial response of the different parts of the natural environment to climate change.

In recent years, various quantitative methods, including artificial neural network (ANN) (Agarwal et al., 2016; Fei et al., 2017), fuzzy cluster (FC) (Tripathi et al., 2015), and expert system (ES) methods (Chavoshi et al., 2013), have been successfully adopted to regionalization studies. Other advanced methods have been applied to regionalization, such as support vector machine (SVM) (Pradhan and Biswajeet, 2013), multivariate spatio-temporal clustering (Ergüner et al., 2019), spatial wavelet analysis (Agarwal et al., 2016), and fuzzy membership functions (Yang et al., 2021). Research into quantitative regionalization has thus moved toward diversification and intelligence, but it is still in the exploratory stage. The aim of these developing methods is to map the land surface quantitatively, rather than to promote quantification of the traditional regionalization method. Given that the organization scheme of regions has been well studied, and that the gradation of indicators is already quantitative handled in traditional regionalization studies, the present study sought to extract and analyze existing rich and complex regionalization knowledge to form quantitative rules and apply this knowledge to make regionalization for China. Rough set is a method that extracts rules expressed as ‘if conditions..., then decisions...’ from a set of data containing conditions and decisions (Leung et al., 2008), and the extracted rules can be used to map objects into decisions according to the conditions of the objects. Rough set methodology can be regarded as a mathematical tool for extracting classification knowledge and has been successfully applied in geoscience (Pan et al., 2010; Liu et al., 2011). Therefore, it has the potential to be used in regionalization studies.

The aim of this study is to extract the regionalization rules of each eco-geographical region in China, which could provide support for the quantification and repeatability of regionalization. To achieve this aim, the potential indicators for each region were first calculated using meteorological data and elevation data in China from 1971 to 2000 (the same period as the existing regionalization results). After that, with the indicators treated as the conditions and the existing regionalization results treated as the decisions, the rough set method was performed to extract rules that connect conditions and decisions. Then the extracted rules were adopted to map regions over China using gridded indicators. Finally, the similarities and differences between the map based on the decision rules and the existing map were analyzed.

The study area is the land surface in China including Hong Kong, Macao, and Taiwan. The terrain of China is characteristic mainly by high in the west and low in the east, covering an area of about 9.6 × 10⁶ km². The Qinghai-Tibet Plateau that locates in the southwest of China is the highest plateau in the world and has a cold climate. In areas outside the Qinghai-Tibet Plateau, the temperature basically decreases from south to north, and the precipitation decreases from southeast to northwest.

The existing regionalization results that were used for rule extraction in this study came from the eco-geographical regionalization of China (Zheng, 2008), one of the country’s representative regionalization studies (Wu et al., 2016). As the eco-geographical regionalization of China was based on multi-annual averages of indicators from 1971 to 2000, this study used data for the same period. Meteorological data from 616 meteorological stations in China provided by the National Meteorological Center of the China Meteorological Administration (CMA; http://data.cma.cn/) were used (Fig. 1). The data collected included temperature, precipitation, relative humidity, number of sunshine hours, and wind speed. Station elevations were obtained from official station information. Although the extraction of regionalization rules was based on the station data, the input of the rules for application in the rough set method was in the form of gridded data. The gridded (1/12°) dataset was obtained by interpolating data from stations by using the thin plate spline method, which has been used in previous studies (Cuervo-Robayo et al., 2014; Yin et al., 2019b). Elevation data for the grid cells were resampled from the 1 km digital elevation model (DEM; Tang, 2019).

Figure 1.  Spatial distribution of the 616 meteorological stations and eco-geographical regions in China from Zheng (2008). Roman numerals indicate temperature zones, capital letters indicate humidity regions, and Arabic numerals indicate eco-geographical regions within the same temperature zone and humidity region

Indicators for the eco-geographical regionalization of China include the ≥10°C growing season (GS), aridity index (AI), precipitation (P), January mean temperature (T₁), July mean temperature (T₇), and elevation (Zheng, 2008). Values of P, T₁, and T₇ were obtained from the meteorological dataset. GS is the number of days in a year for which the mean temperature reaches 10°C, and was calculated using a 5-d running mean method (Deng et al., 2018). AI is the ratio between reference evapotranspiration (ET_O) and precipitation (P) (Budyko, 1974):

ET_O was simulated monthly by using the modified Penman-Monteith model (Allen et al., 1998), for which the radiation was calibrated according to the case of China (Yin et al., 2008).

The data of interest are first organized into a data table whose columns are marked as attributes and rows are as objects. Attributes are distinguished into condition attributes and decision attributes (Pawlak, 2002). In cases where attributes are organized hierarchically, a level-by-level mining strategy is advisable when applying rough sets (Lin et al., 2015). Therefore, this study followed the hierarchical organization of natural domains (NDs)-temperature zones (TZs)-humidity regions (HRs) (or NDs-HRs-TZs) to build the decision tables on three levels.

The NDs (level 1) were the eastern monsoon zone (EM zone), northwest arid/semi-arid zone (NW zone), and Tibetan Alpine zone (TA zone). The initial step involved the delineation of the TA zone according to the geomorphological region of the Qinghai-Tibet Plateau (Li et al., 2013). Then, the decision table was constructed for mapping the objects (stations) into the EM or NW zones.

The zones at levels 2 and 3 are TZs or HRs. In the EM zone, the TZs are zoned latitudinally, therefore, the rules for mapping TZs were extracted first, followed by the rules for mapping HRs in each TZ. In the NW zone, the longitudinal zonation of the HRs means that the rules for mapping HRs were extracted first, followed by the rules for mapping TZs in each HR. For the TA zone, the strategy was the same as that for the EM zone.

A decision rule is a logical description that connects conditions and decisions (Pawlak, 2002). By iterating the combinations of multiple conditions, the decision that occurs under each combination of conditions is determined. The reduction of conditions is accomplished according to the range of conditions required for a decision. Following this, the rule of which conditions are categorical data is extracted. Each decision rule has a consistency value, that is, the probability of the decision being made correctly when its condition occurs, with a certain rule being defined as having a consistency of 100%. A decision algorithm is a set of mutually exclusive and exhaustive decision rules associated with a given decision table.

Rule extraction in this study was based on the following principles: 1) The reduction of conditions was preferred to be the same as the indicator gradation of the existing eco-geographical regionalization (Zheng, 2008); 2) the threshold has better be an integer value; and 3) certain (i.e., 100% consistency) rules were preferred.

With decision rules, new objects can be mapped according to their conditions. The gridded dataset (1/12°) was entered into the decision algorithm to output the zones to which each grid cell belonged, thereby obtaining the eco-geographical regionalization map. The map was then de-noised through a two-dimensional mode filtering algorithm (Bai and Zhang, 1995). A window size of 3 × 3 grid cells was chosen for de-noising.

The map based on the decision rules was compared with both the existing eco-geographical regionalization map (Zheng, 2008) and the map that was based on the commonly used ‘simplified method’. The simplified method is a method of regionalization that takes into account the index range of each TZ or HR, and can be applied to rapid regionalization and quantitative comparison of regional patterns under climate change (Wu et al., 2005; Deng et al., 2018; Ma et al., 2019). In the simplified method, TZs were mapped according to GS, and HRs were mapped according to AI (Zheng, 2008).

The precision rate (PR) and recall rate (RR) were used to evaluate the regionalization results based on the decision rules and those based on the simplified methods, respectively, by comparison of the results with the existing eco-geographical regionalization of China (Zheng, 2008). The PR and RR were calculated for each region and zone. Taking the cold temperate zone as an example, the PR is the ratio of the number of grid cells that correctly predicted the cold temperate zone to the total number of grid cells used to predict the cold temperate zone, whereas the RR is the ratio of the number of grid cells that correctly predicted the cold temperate zone to the total number of grid cells of the cold temperate zone as depicted in the existing regionalization.

where CP (correctly predicted) is the number of grid cells that were correctly predicted to be in the target zone, IP (incorrectly predicted) is the number of grid cells that were incorrectly predicted as being in the target zone, and UP (unpredicted) is the number of grid cells that were incorrectly predicted as not being in the target zone.

The rules at level 1 are for mapping objects into the EM zone or NW zone. The decision algorithm formed by combining these rules contains the conditions of AI, P, GS, and T₁ (Fig. 2). AI and P are the two primary conditions for decision making at level 1, indicating that the difference between the EM and NW zones is characterized more by humidity than by temperature. Those objects located in a humid climate (AI < 1.0) are mapped into the EM zone, and those objects in a relatively arid climate (AI ≥ 2.5) are mapped into the NW zone. For the remaining objects, P, GS, and T₁ should be considered to generate the mapping. In summary, those regions with drier climate, shorter GS, and warmer T₁ are mapped into the NW zone, otherwise into the EM zone.

Figure 2.  Decision algorithm for mapping objects in the eastern monsoon zone or northwest arid/semi-arid zone, China. AI is the aridity index, P is the precipitation, GS is the ≥10°C growing season, T₁ is the January mean temperature.

The condition attributes for mapping TZs in the EM zone are GS, T₁, and T₇ (Fig. 3). From the cold temperate zone to the tropics, the range of the temperature indicators generally increases as the TZ warms, with some exceptions due to the high-altitude stations. These stations generally have a lower value of GS than those in colder zones, although their T₁ values are similar. Therefore, some objects were mapped into the warmer zones if they had a relatively low T₁; for example, those objects with T₁ between 0°C and 1°C. Such cases are more common in the subtropical zones than in other zones, probably because these former zones contain a greater variety of landforms and elevations (Wang et al., 2020b).

Figure 3.  Decision algorithm for mapping temperature zones in the eastern monsoon zone, China. GS is the ≥10°C growing season, T₁ is the January mean temperature, T₇ is the July mean temperature.

The decision rules for mapping HRs were extracted for the mid- and warm temperate zones where there are more than one HRs (Fig. 4). In the mid-temperate zone, the algorithmic logic is to put objects with high moisture conditions into the humid region, and those with low moisture conditions into the sub-humid region (Fig. 4a). For the warm temperate zone, the objects with the driest moisture conditions (AI ≥ 1.5) were mapped into the sub-humid zone (Fig. 4b). As for the other objects, some objects around the Qinling Mountains make the rules complicated, because experts would have merged the junctions of TZs, HRs and landform into one if these junctions are close to make the boundary precise in the existing map (Zheng, 2008). As a result, the rules for mapping HRs in the warm temperate zone also consider T₁ and T₇ to map those objects that are humid but close to the north subtropical zone into the sub-humid region.

Figure 4.  Decision algorithm for mapping humidity regions in the (a) mid-temperate and (b) warm temperate zones in the eastern monsoon zone, China. AI is the aridity index, P is the precipitation, T₁ is the January mean temperature, T₇ is the July mean temperature.

In the NW zone, the semi-arid and arid regions are distributed in the east and west of the zone, respectively. However, some stations in the western mountain regions, where an arid climate should exist, have an AI value similar to that of a semi-arid climate. Therefore, the rules for mapping arid and semi-arid regions could not be extracted accurately using AI alone, and needed to be supplemented by the condition P.

In the semi-arid region, the logic of the rules for mapping TZs was to map warmer objects into the warm temperate zone and colder objects into the mid-temperate zone using GS and T₁ (Fig. 5a). In the arid region, the warm temperate zone in the arid region is distributed mainly in the Tarim Basin, which is covered mostly by desert, meaning that its climate is drier than the mid-temperate zone. Accordingly, the rules for mapping the TZs in the arid region using both temperature and moisture conditions (GS, T₁, T₇, and P; Fig. 5b).

Figure 5.  Decision algorithm for mapping temperature zones in the (a) semi-arid and (b) arid regions in the northwest zone, China. GS is the ≥10°C growing season, T₁ is the January mean temperature, T₇ is the July mean temperature, P is the precipitation.

The logic of the rules for the TZs was to first map the low-altitude (< 2350 m) and warm (GS ≥ 180 d) objects into the mid-subtropical zone (Fig. 6). Then, for the remaining objects, those with higher-temperature conditions were mapped into the plateau temperate zone, whereas those with lower temperature were mapped into the plateau sub-cold zone. The mid-subtropical zone can be identified by using GS ≥ 180 d only with altitude being added to ensure that alpine objects on the plateau are not mapped into the mid-subtropical zone after future climatic warming.

Figure 6.  Decision tree for mapping temperature zones in the Tibetan Alpine zone, China. GS is the ≥10°C growing season, T₇ is the July mean temperature, T₁ is the January mean temperature.

The mapping of HRs in the TA zone could be performed using only AI. The range of AI in the plateau temperate zone and the plateau sub-cold zone was unified to ensure the spatial coherence of HRs among different TZs. The difference is that the condition ‘AI < 1.5’ indicates the humid/sub-humid region for the plateau temperate zone but indicates the sub-humid region for the plateau sub-cold zone.

The natural domains mapped by the decision rules include the EM, NW, and TA zones (Figs. 7a, 7b). The EM zone comprises eight TZs and two HRs, a total of 10 temperature-humidity regions. There are two TZs and two HRs in the NW zone, resulting in four temperature-humidity regions. The TA zone is composed of three TZs and five HRs, giving a total of seven temperature-humidity regions. Because the adopted rules clarified the hierarchical relationship between TZs and HRs according to the existing regionalization map, the TZs and HRs that were mapped using the rules can be combined into temperature-humidity regions. In contrast, the TZs and HRs mapped by the simplified method could not be combined into corresponding temperature-humidity regions because they were mapped separately (Figs. 7c, 7d).

Figure 7.  Spatial distribution of temperature zones (a, c, e) and humidity regions (b, d, f) mapped using decision rules (a, b), the simplified method (c, d), and in the existing eco-geographical regionalization of China (e, f) (Zheng, 2008)

Compared with the regionalization mapped using the simplified method, the regionalization performed using decision rules was more similar to the existing regionalization (Figs. 7e, 7f), with smoother boundaries, fewer scattered regions, and clearer zonation. The simplified method included some independent regions that were probably generated because of local topography, such as the cold temperate zone in the northwest mountains area and the warm temperate zone in the southwest mountains area, and was unable to map the humid/sub-humid region in the Qinghai-Tibet Plateau. These problems did not appear in the regionalization generated using the decision rules method.

Both the PR and RR reveal the advantages of the decision rules method (over the simplified method) for representing the existing regionalization (Figs. 8 and 9). The overall PR equals to the overall RR. The overall PR and RR of the TZs were both 85.37% for the decision rules method, substantially higher than those (66.15%) for the simplified method. The overall PR and RR of the HRs mapped using the rules (90.58%) were also higher than those mapped using the simplified method (77.51%). Compared with the simplified method, the decision rules method has a higher PR for all the TZs, a higher RR for seven of the nine TZs, a higher PR for four of the five HRs, and a higher RR for all the HRs. For the zones/regions that have a lower PR or RR for the decision rules method than the simplified method, the differences in PR or RR were small, and the lower PR or RR did not occur together. Therefore, it can be inferred that the regionalization result of any TZ or HR based on the decision rules was more accurate or at least no worse than that based on the simplified method.

Figure 8.  Precision (PR) (a) and recall rates (RR) (b) of each temperature zone in China mapped using the simplified and decision rules methods

Figure 9.  Precision (PR) (a) and recall rates (RR) (b) of each humidity region in China mapped using the simplified and decision rules method

Of the TZs generated using the decision rules method, the mid-temperate zone was the most similar to the existing regionalization, with both the PR (90.25%) and RR (97.25%) being higher than 90%. The lowest PR and RR values appeared in the mid-tropical (53.33%) and marginal tropical (45.81%) zones, respectively. The large difference may be because of the small areas of these two TZs, and may also be related to the complicated configuration of the range of the tropical zones in southwestern China in the existing regionalization scheme. For HRs based on the decision rules method, the humid and arid regions were defined more accurately than the other regions. The humid region has the highest PR (96.15%) and the second-highest RR (93.40%), whereas the arid region has the second-highest PR (92.00%) and the highest RR (97.55%).

The regionalization map of China generated using decision rules corresponds closely to the configuration of the existing map (Fig. 10), but the boundaries have more bends. In addition, compared with the existing map, the map based on decision rules shows the following differences:

Figure 10.  Eco-geographical regionalization of China. (a) Map based on the decision rules of this study, (b) Existing map (Zheng, 2008)

(1) EM zone: Unlike the existing regionalization map, there is no marginal tropical humid region in southwestern China in the decision-rules-based map. Also, the mid-subtropical humid region has a larger geographic range than in the existing map, expanding by ~1° to the north and south. The north subtropical humid region to the west of 110°E has a width of about 1.5°–3.0° in the existing map, but is squeezed to 0.0°–2.0° by the mid-subtropical humid region and warm temperate sub-humid region in the decision-rules-based map (Fig. 10).

(2) NW zone: The warm temperate semi-arid region in the east of 110°E is 66.88% smaller than in the existing map. West of 80°E, the mid-temperate arid region lies further south compared with the existing map and forms a northeast–southwest-trending belt. Because of this change in configuration, as well as the contraction of the eastern warm temperate arid region, the warm temperate arid region in the decision-rules-based map is 29.15% smaller than that of the existing map.

(3) TA zone: The mid-subtropical humid region in the southeastern Qinghai-Tibet Plateau is mapped into the TA zone, separate from the EM zone, and the area is 51.51% smaller than that of the existing map. A plateau sub-cold arid region appears in the northeastern Qinghai-Tibet Plateau in the decision-rules-based map but not in the existing map. The plateau temperate arid region in the southwestern Qinghai-Tibet Plateau is much small in the decision-rules-based map. In the plateau sub-cold arid/semi-arid region, the proportion of arid region is 27.19% in the existing map and 48.11% in the decision-rules-based map, and the proportion of semi-arid region is accordingly lower in the latter map compared with the former.

This study used the rough set method and a top-down layer-by-layer extraction strategy to extract rules for the eco-geographical regionalization of China. Results show a consistency of more than 85% (85.37% for TZs, 90.58% for HRs) with respect to the existing regionalization map. Therefore, the regionalization generated using the method of this study closely represents the spatial pattern of the existing map.

However, the consistency is not 100%. The main reason for the inconsistency is that our rules do not completely reflect the expert knowledge of vegetation, soil, micro-topography, and elevation, which has been used for the boundary delineation in the existing regionalization scheme (Zheng, 2008). Our methodology is based primarily on climatic indicators, meaning that the rules can be applied to cases for which data on vegetation and soils are difficult to obtain, such as in remote regions and for future climate scenarios. This emphasis on climate likely caused most of the measured inconsistency. For example, there is a plateau sub-cold zone in the northeastern Qinghai-Tibet Plateau in the decision-rules-based map (Fig. 10a). However, experts may have attributed the climatic characteristics of this region to altitudinal zonation, and then mapped it as the plateau temperate zone as in the area of adjacent lower elevation (Fig. 10b). Another reason for the inconsistency may stem from the TZ or HR being a natural region (level 4 unit), for which the conditions include both temperature and moisture indicators. Taking the warm temperate humid region and warm temperate arid region as examples of this, in the eco-geographical map, the former region is distributed only in the Shandong Peninsula and is a natural region, IIIA1, and the latter one is a natural region, IIID1 (Fig. 1). This makes the decision rules for mapping these regions equivalent to those for mapping natural regions at level 4, which are relatively complex (Figs. 4b and 6b).

Despite the differences, the main purpose of the study was to establish a quantified method for rapid, updatable regionalization. Our results, achieved using the rough set methods, closely reflect the overall pattern of the eco-geographical regionalization of China. This study considers the adopted method as producing a sufficiently close representation of the existing regionalization to justify its use for rapid regionalization mapping and incorporating future environmental variation such as climate change.

In addition to the eco-graphical regionalization of China, there are several other authoritative regionalization studies of China that reflect the characteristics of the country’s regional differentiation from other perspectives (Wu et al., 2016). There have been attempts, for example, to delineate the boundary of the Qinghai-Tibet Plateau (Huang, 1959; Zheng, 2008; Zheng et al., 2013), but differences exist, especially regarding the definitions of the eastern, the southeastern, and northern boundaries (Zhang et al., 2002). The delineation of the Qinghai-Tibet Plateau in this study was derived from the geomorphological regionalization of China according to geomorphic types and geomorphic causes (Li et al., 2013). Therefore, the TZ zone in this study contains a mid-subtropical humid region (Fig. 10). In future, with advances in the understanding of the nature of the plateau, the determination of its boundary will be gradually improved (Zhang et al., 2021), which will help improve eco-geographical regionalization.

Another difference in the scheme is the order of consideration of TZ and HR. In other regionalization studies, the order of TZ is generally higher than that of HR, possibly because priority was given to the energy (heat) required for agricultural production during the process of national development. The present study adopted such an approach in the EM zone, where the latitudinal zonation is more obvious than the longitudinal zonation, but not in the western arid/semi-arid zone. The approach using HR then TZ may better express regionalization in the western arid/semi-arid zone, where the east-west span is extensive and there is a single water source (eastern sea area) that drives a pattern of humidity decrease from east to west, and the vegetation cover is distributed consistent with the humidity pattern (Zhao et al., 2019b; Wang et al., 2020a).

In regionalization studies, researchers have disputed the respective northern boundaries of the tropical zone and the subtropical zone. Some studies have pointed out that the tropical zone in China can not be defined only using Köppen’s climate classification (Köppen, 1936) but must more comprehensively consider the conditions of climate, vegetation, soil, and agricultural use (He and He, 1988; Huang, 1992; Qiu, 1993). Of these conditions, the climatic judgment index corresponds to a mean temperature of the coldest month of >16°C, and the rules extracted in this study are consistent with this (Fig. 3). However, owing to differences in which factors are considered (other than climate), there are also differences in the final delineation of the tropical boundary, especially for that in the southern China (Wu and Zheng, 2000; Xu et al., 2018). The northern boundary of the tropical zone in southern China delineated by the rules in this study is distributed between 21°30ʹN to 21°48ʹN, which is similar to the results of Huang (1959), He and He (1988), Zheng (2008) etc. In the southwestern China, other studies have considered the particular conditions on the plateau in Yunnan Province and have used a unique regionalization scheme there compared with other EM regions (He and He, 1988; Zheng, 2008; Xu et al., 2018). This explains why other studies have shown tropical regions in southern Yunnan but were not mapped in the present study. More consideration of the elements of landforms and vegetation in future research may help solve this problem (Zhu, 2013).

Differences in the definition of the northern boundary of the subtropical zone are concerned mainly where the western part of the zone and its delineation from the Qinling Mountains (Yang et al., 2006). Three main views have been proposed: the northern foot, the main ridge, and the southern foot of the Qinling Mountains. Multiple indicators of climate, landform, vegetation, and soil, as well as altitudinal zonation, have been used to demarcate this boundary, which could explain why the northern boundary delineated in this study using only temperature indicators is slightly south of those defined by previous studies (Huang, 1959; Zhao, 1983; Zheng, 2008). Interestingly, recent research based on the geo-detector method that screens indicators and determines the boundaries has also delineated a boundary that lies more toward the south relative to previous boundaries, although that research considered multiple indicators in addition to climate (Kou et al., 2020). Spectra structures of elevation have been interpreted as suggesting that the boundary is more appropriately delineated along the Daba Mountains, which are located adjacent to the Qinling Mountains (Zhao et al., 2019a). Therefore, although it is difficult to ascertain which boundary is more accurate at present, different approaches clearly yield different results, with the multiple perspectives probably serving specific interests and purposes. Future research may need to better handle multi-feature integration and the challenge of judging boundaries in transitional areas.

Decisions need to be made during the processes of delineating the boundaries. In previous authoritative regionalization studies, the decision-making step generally contains complex experience and knowledge of experts that is expressed in semi-quantitative form (Fu et al., 2001; Zheng, 2008). As shown in the present study, through the rough set method, this experience and knowledge can be extracted and stored quantitatively in the form of decision rules. Our approach can unify the human decision-making process of regionalization and thus facilitate the comparison of regionalization results between different periods and scenarios. The expert knowledge contained in regionalization could also be extracted and stored through other methods, such as the ANN and fuzzy membership functions (Zhu et al., 2018; Yang et al., 2021). The development and improvement of such methods may be one of the major directions of geographical regionalization research in the future.

In applications of, or research based on, rough sets, a feature (attribute) selection algorithm is used to maximize the information that can be provided by the features (Maji and Paul, 2011; Raza and Qamar, 2018). To construct more realistic extracted rules and apply them more effectively, attributes in the rules should be representative and should be selected according to objective laws or aspects of interest (Pawlak, 2002; Amin et al., 2017; Xiao et al., 2018). This study considered the above principles of selection and selected conditional attributes as part of the methodology of regionalization. Accordingly, the extracted rules referred to three important parts of the methodology: the hierarchical organization relationship, selection of indicators, and indicator gradation. Therefore, the rules are credible and can restore the decision-making process of the existing regionalization using the rough set method. Compared with studies that have mapped each region using a single indicator (Feng et al., 2014; Deng et al., 2018), the decision rules extracted in the present study combined multiple indicators to delineate the boundaries of regions, thereby better handling the complexity of regional characteristics and the regionalization process.

With accelerating climate change in the second half of the twentieth century (IPCC, 2013), values of temperature indices for eco-geographical regionalization have increased markedly (Barichivich et al., 2012; Blinova and Chmielewski, 2015; Spinoni et al., 2015a). Furthermore, changes in the values of water indices have modified regional differentiation (Zarch et al., 2015; Yin et al., 2018). Consequently, the terrestrial TZs and HRs have undergone significant shifts in boundaries (Mahlstein et al., 2013; Spinoni et al., 2015b; Huang et al., 2016). These shifts may continue or intensify during the remainder of the 21st century (Feng et al., 2014; Belda et al., 2016). The anticipated change in of climate means that regionalization will need to be updated more frequently. The rule extraction method developed in this study constitutes a repeatable and quantitative approach for delineating the boundaries of eco-geographical regions and thus is suitable for incorporating the variation introduced by climate change. Our future work aims to incorporate climatic change scenarios into regionalization, to generate regionalization results that more comprehensively reflect the distribution of natural elements, and to reduce the impact of uncertainty of rules. The specific reasons for the existence of uncertainty could be analyzed and clarified by adding information gained from field investigations around uncertain boundaries.

This study used the rough set method with an indicator system and the hierarchical organization of the eco-geographical regionalization of China to extract regionalization rules from meteorological station data. The conditions were the length of the ≥ 10°C thermal growing season (GS), aridity index (AI), January mean temperature (T₁), July mean temperature (T₇), precipitation (P), and altitude. The following results were obtained.

(1) Decision rules were extracted level by level, so that the application of rough sets could reflect the hierarchical organizational of the regionalization. Both the eastern monsoon (EM) zone and the Tibetan Alpine (TA) zone used temperature zones as the level 2 units and humidity regions as the level 3 units. In the northwest semi-arid (NW) zone, humidity regions and temperature zones were the units at levels 2 and 3, respectively.

(2) The eco-geographical regions mapped by the rules give a close representation of the existing regionalization scheme of China. At level 1, the main conditions used were AI and P, and the secondary conditions were GS and T₁. At levels 2 and 3, the conditions for generating temperature zones were mainly GS, T₁, and T₇, and those for generating humidity regions were AI and P. The temperature zones and humidity regions generated by the decision-rules-based method showed 85.37% and 90.58% consistency with the zones and regions of the existing regionalization, respectively.

(3) Using the proposed rough set method, the same pattern of regions would be generated so long as the regionalization scheme is the same. Therefore, using this method, changes in the geographical regions in different periods and under different climate change scenarios can be detected objectively.