The Association between Rainfall and Taxi Travel Activities: A Case Study from Wuhan, China

Rainfall has a signifcant impact on urban population mobility, posing great challenges to trafc management and urban planning. An understanding of this infuence from multiple perspectives is urgently needed. In this study, we devised a multiscale comparative research framework to explore the spatiotemporal efects of rainfall on taxi travel patterns, aiming to provide a new perspective on the investigation of rainfall’s impact on urban human mobility. More specifcally, at the macroscopic scale, we computed taxi travel indicators across the entire study area and used kernel density estimates to observe the spatiotemporal distribution patterns infuenced by rainfall. Subsequently, complex trafc networks were constructed by considering urban road intersections as nodes and combined with visualization methods to understand changes in taxi travel patterns visually at the microscopic level. We selected Wuhan City, a typical urban area in southern China with frequent rainfall, as the study area and used meteorological data along with a large volume of taxi spatiotemporal trajectory data for investigation. Results indicated a 4.16% decrease in weekly travel volume due to rainfall, with a 3.96% decrease on workdays and a 4.64% decrease on weekends. However, nighttime rainfall between 19:00 and 22:00 on weekdays increased the demand for taxi travel. Furthermore, the impact of rainfall on weekends exceeded that on workdays, restricting people’s mobility and leisure activities, resulting in reduced travel to recreational tourist spots and commercial pedestrian streets. Rainfall altered residents’ travel preferences to some extent, with more residents choosing taxis during rainy weather, which led to decreased transportation efciency and increased trafc congestion. Tese fndings contribute to a deeper understanding of the complex relationship between population mobility patterns and the urban ecological environment, providing valuable insights for planning resident travel and taxi dispatching under adverse weather conditions.


Introduction
Te city embodies a complex system where humans navigate, interact with urban infrastructure, and generate a myriad of fows that refect their trajectories [1].Understanding the nature of these fows ofers invaluable perspectives and insights for addressing socioeconomic issues such as urban planning, transportation forecasting, and epidemic prevention and control [2][3][4][5][6].Traditional methods for analysing population mobility often rely on costly, subjective, and spatially limited questionnaire surveys [7][8][9].In recent years, the development and widespread adoption of location services and communication technologies have presented new opportunities for the timely collection and analysis of large-scale mobility data [8,10].Technologies like smart cards, shared bicycles, mobile phone signals, social media check-ins, and taxi trajectories contribute substantial urban population mobility big data, ofering rich location and activity information at the individual level [1,[11][12][13].In comparison to traditional approaches, big data are more accurate, objective, comprehensive, cost-efective, and easily accessible [14,15].It has emerged as the primary dataset for trajectory data research and applications, providing abundant information for studying dynamic urban changes [6].
Taxis, serving as a door-to-door, round-the-clock mode of transportation, fulfl the dense and recurrent daily travel needs within cities, playing a crucial role in urban public transportation systems [16].According to statistical data from 2022, taxi passenger volume in China reached approximately 20.82 billion trips, constituting 27.6% of the total urban passenger transportation and ranking as one of the primary choices for residents' travel [17].Presently, taxis are equipped with GPS recording devices that promptly collect more precise spatiotemporal information, including passenger boarding and alighting locations, during journeys [11].Difering from buses and rail transit, taxis operate without constraints of routes and schedules, ofering the most fexible and extensive trajectory data based on passenger preferences [18,19].Taxi trajectory data exhibit higher accuracy and involves fewer privacy concerns compared to other modes of transportation.Tis characteristic aligns taxi trajectory data more closely with the genuine intentions of passenger travel, allowing it to authentically portray the spatiotemporal characteristics of residents' mobility and the travel patterns of taxis.
Weather conditions, as an integral part of the urban ecosystem, exert a signifcant infuence on the daily travel patterns of residents and population movements [20][21][22][23][24]. Terefore, comprehending how adverse weather afects human travel patterns contributes to enhancing public transportation services and better meeting passengers' travel needs under diverse weather conditions.Various meteorological factors have been well researched in the transportation domain, including rainfall [25,26], snowfall [22], temperature [27], and wind [28], either individually or in combinations [29][30][31].Existing studies primarily employ exploratory and descriptive methods, such as statistical charts, graphs, and summaries, to analyse and describe data characteristics under diferent weather conditions [32].For instance, Liu et al. quantifed the impact of weather on ridehailing taxi passenger volume, fnding that a 1 mm increase in precipitation led to a 0.39% rise in trafc volume, while a 1 m/s increase in wind speed resulted in a 1.04% decrease in trafc volume [22].Autoregressive Distributed Lag models, built on statistically summarized data, are used for quantitative analysis of the sustained efects of snowfall on taxi operations [33].While these methods provide overall statistical characteristics of the dataset, aiding in uncovering spatiotemporal distribution patterns of taxi activities and population mobility under weather infuences [34], simple quantitative analyses of travel features and large-scale fuzzy analyses fall short in addressing the current complexity of human mobility dynamics.A comparative analysis of taxi travel activities and population mobility spatiotemporal distribution characteristics under diferent weather conditions, especially through a multiscale and multidimensional approach, is lacking.
Terefore, we utilized taxi trajectory data to construct a complex geographic spatial network at the street level.Graphs and network characteristics extracted from the trajectory data were investigated for their structural properties and the interactions between these properties using graph theory and complex network-related methods.Spatial statistical analysis methods were combined to analyse taxi travel metrics, establishing a multiscale, multidimensional analytical framework.Tis framework was applied to investigate the impact of rainfall on taxi travel activities and population mobility patterns, providing a bottom-up perspective for studying population mobility patterns under the infuence of rainfall.Subsequently, we applied our comparative research framework to the rain-prone city of Wuhan, collecting taxi trajectory data and meteorological data within the study area.Te taxi data were categorized into four scenarios: weekdays with clear weather, weekdays with rain, weekends with clear weather, and weekends with rain.We aimed to explore the feasibility of using taxi trajectory data to investigate the impact of rainfall on population mobility.To scrutinize and dissect the spatial disparities of fundamental taxi travel metrics on a macroscopic level, and subsequently, to assemble a comprehensive trafc network on a microscopic scale, a meticulous examination and comparative analysis of the alterations in network confguration induced by rainfall which is achieved through a fusion of network attribute metrics and visualization techniques, is involved.

Application of Taxi Trajectory Data.
In recent years, the widespread development of location services and communication technologies has made the collection and study of taxi trajectory data possible.Many studies use this information to identify trafc congestion [35,36] and estimate trafc fows [37], which helps to understand urban mobility patterns from a social perception perspective, improve trafc, and assist managers in taking emergency measures [38].Furthermore, the unique advantages of taxi trajectory data in studying urban population travel patterns and population mobility have garnered signifcant attention.Researchers explore crowd movement patterns [39] and employ mathematical and statistical methods to focus on collective mobility patterns at the urban scale by mining trafc hotspots and tracking trafc trajectories between key areas [35].It is noteworthy that the application of taxi trajectory data extends beyond the realm of intelligent transportation, gradually seeking comprehensive integration with other professional felds, such as extracting urban functional structures [38,40,41].For instance, Hu et al. established a geographical semantic analysis framework to extract trafc interaction information from taxi data, delineating urban functional zones at the road level [40].Tey analysed the respective strengths and interactions between taxis and other modes of transportation.Combining Point of Interest (POI) data and road network data, taxi trajectory data have been used to investigate taxi demand travel patterns and associated infuencing factors using grid partitioning and geographic weighted regression models [11].
Spatial statistical methods provide an intuitive means for researchers to comprehend the overall distribution characteristics of datasets, commonly employed in the analysis of taxi trajectory data [42,43].Exploratory and descriptive techniques, such as statistical charts, graphs, and summaries, are utilized to analyse and depict data features.Additionally, point clustering analysis on taxi origin and destination locations aids in identifying popular areas, enabling the recommendation of optimal passenger origin points to taxi 2 Journal of Advanced Transportation drivers [44].Chen et al. proposed a two-stage clustering algorithm to identify candidate areas in urban space, integrating taxi trajectory data to estimate taxi travel routes and destinations [21].Various regression models are employed in studies predicting the ftting of taxi trajectories to passenger mobility [45,46].By ftting the distribution of passenger boarding points, these models forecast spatiotemporal changes and waiting times for passengers in hotspot areas [47].When facing unknown overall data characteristics in taxi trajectory data, spatial statistical methods efectively capture the dataset's overall statistical features, revealing spatiotemporal distribution patterns of taxi activities and population mobility [34].In addition, Zhang employed machine learning methods, training graph convolutional networks on road network information and taxi trajectory data [48].Tis approach extracted spatiotemporal features of roads and accurately predicted taxi fow at city intersections using the Taxilnt prediction model.Nonnegative matrix factorization methods were used to study the spatial supply patterns of taxis in Wuhan, refecting the impact of taxis' selforganized operational behaviour on urban residents' travel characteristics [33].Liu et al. introduced community detection methods, utilizing collective travel data extracted from taxi GPS trajectory data to explore urban travel patterns and city structure [49].It is evident that taxi trajectory data, through diverse methodologies, signifcantly contributes to the study of population mobility patterns, providing robust support for urban transportation.

Impact of Weather on Transportation Systems.
As a crucial component of environmental factors, weather signifcantly infuences transportation activities and urban population mobility [50].In comparison to localized events such as road construction and trafc accidents that afect travel, weather variations have a broader impact on the entire urban transportation network, compelling individuals to change their travel plans or even cancel them [20,51].
Given the intricate and variable nature of weather factors, current research predominantly focuses on the impact of various weather elements on taxi travel activities and crowd mobility patterns [52].For instance, Li et al. investigated the lag efects of snowfall on taxi operations using GPS data, revealing substantial delayed efects induced by snowfall [22].Caceres et al. developed an efective probability model utilizing ETC toll data to estimate the distribution of travel times on highways under diferent weather conditions [53].Disastrous weather events like typhoons and storm surges bring destructive impacts to transportation [22,[54][55][56].
Additionally, rainfall exerts a more pronounced efect on residents' daily travel patterns [23,57], causing delays during normal travel times and infuencing drivers' moods, resulting in changes to the spatiotemporal distribution of trafc demand [58][59][60].Smith's observations of trafc sequencing on the Hampton Highway found that light rain led to a 4%-10% reduction in highway capacity, while this fgure is 25%∼30% in heavy rain [59].Lam incorporated rainfall intensity as a parameter into generalized speed-fow and speed-density models to analyse its impact on the fow-speed-density relationship on urban roads in Hong Kong [60].Sun quantitatively studied the efects of rainfall on taxi calling and operations in Shanghai using taxi GPS data [24].Tey attempted to identify the two most signifcant factors infuencing these efects through a multiple regression model: passenger numbers and taxi availability.Most studies have examined the infuence of weather factors on various transportation modes concerning travel frequency, travel methods, travel speed, and travel time [42,43].However, there is a defciency in research on the spatiotemporal distribution characteristics of taxi travel activities under diferent weather conditions from a multiscale, multidimensional perspective.

Research on Complex Networks.
A substantial volume of trafc fow enables researchers to simulate entire cities within a spatially embedded transportation network, offering a bottom-up and objective perspective for studying population mobility patterns [61].By integrating mathematical statistical analysis [62] with spatial visualization of network attribute characteristics [63], geospatial complex networks provide a more intuitive understanding of subtle variations in trafc fow.For instance, Xin et al. studied the impact of the COVID-19 pandemic on the bike-sharing system and population mobility in New York City at different scales based on geospatial network analysis [1].Yang et al. utilized geographic spatial complex networks to study the changes in shared bicycle systems resulting from the operation of a new subway line in Nanchang [6].In the aviation sector, Dai et al. examined the evolving structure of the complex air transportation network in Southeast Asia from 1972 to 2012, considering both topological and spatial changes [64].Geospatial complex networks have also been applied to maritime transport, shedding new light on the factors afecting port and shipping development [65].Supported by taxi GPS trajectory data, complex networks can conduct in-depth analyses of taxi transportation processes and activity networks at a more refned spatiotemporal scale.Some studies have recognized the value of exploring the complex characteristics of networks formed by taxi activities using GPS trajectory data [33,66,67].Fu et al. constructed a type of urban travel complex network based on taxi operational GPS trajectory data.Tey employed directed weighted complex network metrics to analyse the complexity of the taxi travel trajectory network structure and spatial analytical features [66].Kang et al. systematically studied the spatial supply patterns of taxis using complex networks and nonnegative matrix factorization methods [33].Peng et al. utilized taxi data and trafc nodes to build a complex transportation network, analysing the impact of rainfall on urban population movement under diferent modes [67].However, previous research has exhibited arbitrary spatial unit division, posing challenges in defning nodes and edges due to signifcant diferences in unit scales.Additionally, the nonuniform distribution of taxi trajectory data across urban areas may lead to insufcient understanding of characteristics and connectivity in certain regions during network analysis.

Study Area.
Te analysis for this study utilized taxi track data for June and July 2014 from Wuhan City, which is the most populous in Central China and is afected by frequent rainfall.Tere are thirteen administrative regions in Wuhan City, including Jiang'an, Jianghan, Qiaokou, Hanyang, Wuchang, Qingshan, Hongshan, Dongxihu, Hannan, Caidian, Jiangxia, Huangpi, and Xinzhou.Since the majority of taxi trajectory data is concentrated within the Tird Ring Road area of Wuhan City, we selected this region as our study area, which also serves as the city centre.Figure 1 shows the study area.As of 2014, the city of Wuhan, where the sharing economy and online taxis were not yet widespread, relied mainly on buses, taxis, and rail transport to move people, with 16,597 taxis operating in the city at the time.

Data Description.
Tree datasets were used in this study: the taxi GPS trajectory dataset, the road network dataset, and the daily rainfall dataset; all datasets were selected from Wuhan City for June and July 2014.Every few seconds, 16,597 taxis uploaded a status data entry to the database through their GPS devices.Each data entry consists of 12 felds, including taxi ID, time, longitude, latitude, operational status, instantaneous speed, and direction.Te road network dataset, obtained from the ofcial website of OpenStreetMap (OSM), provided the required transport network and road intersection data to align with our trajectory data on the map.Te daily rainfall dataset was acquired by the Wuhan City Meteorological Bureau and efectively refects the city's rainfall conditions.Following the classifcation of daily rainfall by the China Meteorological Administration, rainfall below 10 millimetres was defned as light rain, which has minimal impact on trafc and human activities [68].Terefore, for this study, we prioritized selecting rainfall data ranging from moderate rain to heavy rain.To facilitate comparative analysis under similar conditions, we selected two complete weeks of data from the available dataset-one with clear weather and the other with rainy weather.Te selected dates may not be consecutive but must include a full workweek and weekend.Te chosen dates are presented in Table 1.

Data Preprocessing and Matching.
Te richness of trajectory data does not eliminate the scarcity of activity information.Te original dataset contains personal behavioural data of taxi drivers, but only a small portion of it is useful for our study [19].Terefore, a simple and efective data preprocessing step is necessary to ensure the accuracy of research results.First, the 12 felds of each status data entry will be reduced to fve felds for efcient data processing.Tese fve felds include vehicle ID, latitude, longitude, UTC, and taxi operating status.Te vehicle ID, latitude, and longitude determine the vehicle information and real-time location, while UTC records the duration of the trip.Te operating status is used to diferentiate between the driving and passenger-carrying states of the vehicle.All these elements are crucial for identifying each trip route.Based on this, the taxi trajectory data are extracted.We arrange all vehicle IDs for the same day in chronological order, and based on the sorted taxi operating status data, we extract the vehicle's travel trajectory and origin/destination points.Identifcation of origin/destination points relies on the continuous changes in diferent states.When the operating status changes from 0 to a continuous 1, it is recorded as the origin point (O point), and when the continuous status changes from 1 to 0, it represents the destination point (D point) of the trip.Travel time is the time diference between the O point and the D point, while the travel distance is the cumulative distance from the O point to each waypoint and the D point.Tese steps are repeated until all taxi travel trajectories are extracted, and the number of passengers carried by the vehicles on that day is recorded.Finally, to maintain data quality and ensure result accuracy, it is necessary to clean erroneous travel trajectory data, excluding data loss or redundancy caused by GPS device malfunctions, building obstructions, and similar situations during taxi journeys.Tree types of data should be cleaned: (1) travel time less than 2 minutes; (2) average speed exceeding 120 km per hour; and (3) travel distance outside the range of 1 to 100 kilometres.After data preprocessing, approximately 30,000 trajectory data entries are obtained on average per day for the study.Each trajectory data entry represents a complete trip, containing information such as the taxi's origin/destination locations, travel time, and travel distance.
Te accuracy error of GPS devices can lead to taxi trajectory points deviating from the urban road network, impacting data quality, and this type of error cannot be eliminated through data preprocessing.Te purpose of map matching is to accurately align taxi trajectory points with the urban road network.Currently, map matching algorithms involve two crucial processes: fnding target features and projecting target points onto these features.Commonly used matching algorithms include projection algorithms, geometry-based algorithms, probability statistical algorithms, and fuzzy logic algorithms.Te "point-to-line shortest path" method employed in this paper belongs to the category of geometry-based algorithms, specifcally pointto-line matching.Te principle involves calculating the projection distance of GPS location points onto all candidate routes, comparing it with the actual distance of the matching road segment, and selecting the candidate route with the shortest distance as the target route.Te mathematical point-to-line model is illustrated in Figure 2.
In practical implementation, to reduce data processing, we designate the O point of travel trajectories as the reference dataset for map matching, with the following specifc steps: (1) set a 500-meter maximum bufer distance as the minimum projection distance to eliminate some mismatched points; (2) vertically project trajectory points onto all target road segments within the defned range; and (3) match the target road segment with the smallest projection distance and record the position information of the projected point on the target road segment.Finally, the position of the projected point is obtained as the matching point corresponding to the trajectory point.

Comparative Analysis Framework.
Our comparative analysis framework consists of three general steps, as depicted in Figure 3. Firstly, we conduct data processing on taxi GPS trajectory data, OSM road network data, and meteorological rainfall data.Tis involves tasks such as feld simplifcation, extraction of taxi trajectories, and cleaning trajectory data.Subsequently, we employ the "point-to-line shortest path" map matching method to align taxi trajectory points with road network data.Secondly, we perform spatiotemporal data analysis at both macro and microscales.At the macroscale, our emphasis lies on the overall statistical analysis of the data.Spatial statistical methods are utilized to statistically analyse taxi travel volume, travel time, and travel distance, with the visualization of data clustering characteristics through kernel density.At the microscale, we construct a complex geographic spatial network using road intersections as nodes.We analyse the diferences in relevant network metrics at the street level during nonrainy periods, detect network communities, analyse the spatiotemporal distribution of detected communities, and conduct spatial visualization analysis of community metrics using Graph.Finally, through multiscale spatiotemporal and network analyses, we compare the diferences between sunny and  rainy days across diferent time ranges, aiding in the study of the impact of rainfall on taxi travel activities and urban population mobility.

Macroscale Analysis.
At the macroscale, we initially conduct spatial statistical analysis of indicators related to taxi travel characteristics in the form of visualizations through charts.Subsequently, the spatial distribution and clustering features of O and D points are visualized using kernel density estimation methods.

Spatial Statistical Analysis.
Spatial statistical analysis provides an intuitive means for researchers to comprehend the overall distribution characteristics of the dataset, aiding in the selection of appropriate analytical models for subsequent trajectory data analysis [66].Te crucial indicators refecting the patterns of taxi travel include trip volume, travel time, and travel distance.Te trip volume serves as a tangible metric for assessing urban population mobility, exhibiting temporal variability.High trip volumes to some extent refect the high fuidity of the urban population, with signifcant susceptibility to infuencing factors, rendering it of considerable research value.Travel time is an indicator capable of refecting diferent travel purposes, as diverse purposes lead to varied spatiotemporal distribution patterns of travel behaviour.Additionally, travel distance stands as one of the primary factors infuencing residents' choice of travel modes.For instance, residents typically opt for ecofriendly modes such as bicycles or public buses for shortdistance travel, while for long-distance journeys, ideal scenarios often involve minimizing travel time, leading to choices like taxis or subways.Metrics such as average trip volume and average usage duration not only facilitate the analysis of passenger travel behaviour patterns and population mobility but also assist taxi companies in dispatch planning to meet the operational needs of daily taxi services.

Kernel Density Analysis.
Te kernel density analysis method is employed to assess the spatial clustering of elements throughout the entire study area.Tis method utilizes discrete points to generate continuous surfaces, revealing regions where elements are more concentrated [34].Te kernel density analysis facilitates the extraction of hotspots in taxi aggregation [69] and the analysis of the spatiotemporal distribution patterns of taxi behaviour [70].In comparison to commonly used point density calculation methods that ignore spatial distribution heterogeneity or spatial continuity (such as sampling methods, Voronoi  6 Journal of Advanced Transportation diagram methods, etc.), the kernel density analysis method considers both spatiality and the decay efect of continuity [4,71].It yields smoother and more reasonable boundaries for the extracted areas.Te formula for kernel density analysis is where k(x) is the kernel function, h is bandwidth, and n is the number of discrete points in the bandwidth range.
Previous studies have shown that the selection of bandwidth is generally positively correlated with the dispersion of the points and is related to the scale of the analysis [72].
Generally, larger values of h correspond to the analysis at the macroscale that refects the trend distribution, whereas smaller values of h help fnd local characteristics.In practice, therefore, h must be adjusted to suit the demands of the analysis and the actual results.

Microscale Analysis.
At the microscale, we constructed a complex geographic spatial network at the street level, focusing on analysing network statistical metrics related to complex networks.Subsequently, the changes in community structures under diferent conditions were examined.

Construction of Complex Transportation Networks.
Complex networks represent an abstraction model for understanding complex systems, where entities are abstracted into nodes and relationships between entities into edges.Tis model provides a closer approximation to the real spatial distribution and natural structure of road networks in urban spaces.In the context of taxi transportation, the vast amount of trajectory data form a taxi trafc network, where the spatial positions of nodes are defned by origin and destination locations, and edge weights refect the strength of connections between nodes [62,66].Tis spatial network, constituted by the travel behaviours of taxis, falls into the category of typical transportation complex networks [73].
Analysing its structural and topological interactions using graph theory and methods related to complex networks can reveal intricate relationships within the transportation system.
Te uneven distribution of road intersections in the road network does not align with the actual origin and destination points of taxis.Terefore, to construct a more realistic complex network, road intersections need to be extracted based on general patterns of residents' travel.Te methodology involves extracting all road intersections in the Wuhan road network, clustering intersections on road segments shorter than 300 meters into a single intersection, and equally dividing road segments longer than 1000 meters into smaller sections to maintain lengths between 300 and 1000 meters.Taxis' origin and destination points are then clustered onto the corresponding road intersections.Each taxi trip from O to D represents a connection, resulting in a directed and weighted complex transportation network.In this network, road intersections serve as nodes (N), and each taxi trip between two intersections is an edge.Te weight of each edge represents the number of taxi connections between the intersections, providing insight into the total volume of trips for each node.Te fnal step involves visualizing network characteristics using graph theory and complex network methods.By examining the dynamic changes in network attributes, we can reveal how rainfall infuences taxi travel activities and population mobility.

Community Detection.
Community detection is an algorithm used to identify structural communities within complex networks.A community represents a subset of nodes in a complex network, and the entire network can be considered composed of multiple communities.Nodes within the same community exhibit tighter connections, while connections between communities are relatively sparse.In this study, a community's node set corresponds to a set of road intersections with higher frequencies of travel connections in the taxi trafc network.Community detection relies on high-strength connections between nodes rather than spatial proximity.In this context, it identifes subsets of road intersections with frequent travel connections.Te detected communities are then analysed for their spatial distribution through spatial visualization.Analysing the dynamic changes in community structure under different weather conditions and periods provides valuable insights into the impact of rainfall on taxi travel activities and population mobility.Tis approach is particularly crucial for understanding the infuence of rainfall on taxi travel and population mobility.

Statistical Analysis of Travel Data.
In this study, the analysis is conducted on an hourly basis to compare the travel volumes during weekdays, weekends, and diferent periods of sunny and rainy days within a week (Figure 4).Te abbreviations used in the fgure are as follows: SAWE and RAWE represent sunny weekend days and rainy weekend days, SAWD and RAWD represent sunny weekdays and rainy weekdays, and SDAW and RDAW represent the sunny week and rainy weeks, respectively.Tese abbreviations have the same meanings in the following charts.
From Figure 4, it can be observed that rainfall reduces the taxi travel volume, with a more pronounced impact on weekends.Rainfall not only decreases the taxi travel volume but also delays the peak travel time, leading to a certain degree of trafc congestion.Specifcally, rainfall causes a 3.96% reduction in taxi travel volume on weekdays (Figure 4 .During weekdays, commuting and work-related travel constitute a signifcant portion, and rainfall primarily afects the timing of people's travel.For example, on sunny days, the travel peak occurs between 7 a.m. and 2 p.m., while on rainy days, the peak shifts to between 8 a.m. and 1 p.m. Unlike the continuous rise on sunny days, rainy days exhibit noticeable fuctuations in travel volume, reaching a higher Journal of Advanced Transportation level than sunny days at 9 a.m.Tis is closely related to the concentration of rainfall between 7 a.m. and 8 a.m.People often choose to delay their travel during heavy rainfall, resulting in a higher taxi demand during necessary commuting hours to minimize the impact of rainfall.With decreasing rainfall, there is minimal impact on residents' travel between 2 p.m. and 7 p.m.However, rainfall significantly infuences the choice of nighttime transportation. On weekdays with rainfall, more people opt for taxis between 7 p.m. and 10 p.m., resulting in a 4.17% increase in taxi travel volume.In contrast, rainfall considerably diminishes people's desire to travel on weekends, particularly between 7 a.m. and 10 p.m. Te travel volume on rainy days is signifcantly lower than on sunny days, with low peaks at 11 a.m. and 5 p.m. Notably, 11 a.m.coincides with the peak rainfall, and after 5 p.m., as rainfall decreases, travel volume increases, showing no signifcant diference from sunny days.Additionally, between 7 p.m. and 10 p.m. on weekends, taxi travel volume decreases by 5.47%.Tis could be attributed to people engaging in leisure activities on weekends, with the fexibility to choose travel times and destinations.Rainfall limits people's travel options, making them more inclined to choose cost-efective means like walking, especially when rainfall is minimal.On sunny days, people are more likely to engage in long-distance recreational activities, resulting in higher demand for taxis.Terefore, with the average travel volume on weekends exceeding that on weekdays (Figure 4(d)), we can understand that rainfall leads to a lower attenuation rate of travel volume on weekdays than on weekends, indicating a more pronounced impact on weekends.
Building upon that, we further conduct a statistical analysis of travel duration frequency (Figure 5).It is evident that taxi trips predominantly exhibit short durations, and rainfall extends the travel time, leading to an increase in the frequency of short-duration trips.As depicted in Figure 5, the travel frequency for all conditions peaks within 6 minutes and gradually decreases over time.During weekdays, the total frequency within 30 minutes for both sunny and rainy days accounts for 87.75% and 87.34%, respectively, which is higher than the respective percentages of 87.58% and 85.73% for weekends during the same period.Tis indicates that short-duration trips dominate taxi travel, and more people choose taxi travel during weekdays, with rainfall having a greater impact on weekends.Additionally, rainfall increases the frequency of travel durations by 6 minutes, particularly during weekdays.Tis suggests that rainfall to some extent increases the number of longduration trips and alters people's travel modes, such as switching from cycling to taking a taxi.Te trafc congestion issues introduced by rainfall may also be a signifcant factor contributing to the prolonged travel times.
Moreover, we analysed the travel distances of taxis in kilometres (Figure 6).We defned trips with a distance exceeding 10 kilometres as long-distance travel.Overall, regardless of weather conditions (sunny or rainy) or weekdays/weekends, the travel frequency decreases as the travel distance increases, and the rate of change becomes smaller.During weekdays, the total frequency of trips within 10 kilometres for sunny and rainy days is 81.53% and 81.3%, respectively.Rainy days have a lower travel frequency than sunny days for distances up to 7 kilometres, but as the travel distance increases, the frequency of rainy days gradually surpasses that of sunny days.Te results for weekends are similar to weekdays, with total frequencies within 10 kilometres being 81.36% and 79.47% for sunny and rainy days, respectively.However, it is only after 9 kilometres that the frequency of rainy days surpasses that of sunny days.Tis indicates that short-distance trips dominate taxi travel, and rainfall increases the frequency of long-distance travel.Due to the impact of rainfall, the frequency of short-distance travel decreases, especially on weekends.

Analysis of Spatial and Temporal Distribution. Te spatial distribution of OD points exhibits variations, prompting an investigation into the spatiotemporal distribution patterns of passenger fow at O point and D point locations.
A kernel density interpolation analysis was conducted on the quantity of OD points during both rainy and nonrainy weather conditions across weekends, weekdays, and the entire week (Figure 7).
As depicted in Figure 7, the hotspots of taxi origin and destination points in Wuhan City are primarily concentrated around the train station, central business district, commercial streets, Optics Valley Square, and some small scenic spots.Te variations in hotspot areas across the series of maps are not very pronounced.However, diferences emerge during rainy weekends, where the hotspot areas for D points (Figure 7(b)) exhibit a more difuse pattern compared to O points (Figure 7(a)) in larger areas.In smaller hotspot areas, the kernel density values for D points are lower than those for O points, and the range is slightly reduced.Tis conclusion holds for other temporal dimensions and weather conditions.For instance, on rainy weekends, the comparison between O points in rainy and nonrainy conditions reveals that in larger dense areas, the rainy day O points' hotspot areas are more dispersed than those on sunny days.In smaller dense areas, the kernel density values for rainy days are enhanced compared to sunny days, leading to a contraction in the region.
Upon this foundation, we subtracted the number of taxi trips on rainy days from that on sunny days within the same road intersections, followed by conducting kernel density interpolation analysis.Negative values indicate a reduction in trips on rainy days, whereas positive values signify an increase in trips.As illustrated in Figure 8, rainfall exhibits distinct spatial variations in its impact on weekends and weekdays.Rainfall does not extinguish residents' desire to travel on weekends, with a preference for taxi rides to comprehensive shopping malls or other city attractions.Consequently, high-density regions for O and D points on weekends (Figures 8(a) and 8(d), highlighted in red) are mainly distributed near the train station and residential areas.Simultaneously, taxi trips originating and terminating in business districts, such as Wangjiawan and Xudong, experience a minor increase on rainy days.Notably, on weekdays, high-density regions for O and D points (Figures 8(b) and 8(e), highlighted in red) are also concentrated near the train station and business districts.However, the increase in the vicinity of the train station and residential areas is signifcantly lower than that on weekends.Conversely, there is a sharp increase in taxi trips near business districts, particularly around the Xudong business district.Tis is attributed to the densely populated residential areas nearby and the absence of a subway in this area in 2014.Rainfall has heightened the demand for taxis in this region, especially for essential commuting or work-related activities.
Furthermore, regardless of weekdays or weekends, there is a decrease in taxi trips near leisure and entertainment attractions and commercial pedestrian streets due to rainfall.For instance, the commercial pedestrian street in Jianghan District consistently registers as a low-density area.Near the South Lake College Town, the impact of rainfall remains optimistic, with minimal changes in travel volume.Te areas around Wuhan University and Huazhong University of Science and Technology experience noticeable fuctuations only on weekdays.In summary, rainfall increases taxi travel near train stations, business districts, and residential areas while decreasing residents' inclination to visit leisure tourist spots and commercial pedestrian streets.Additionally, rainfall prompts more residents to choose taxi rides, particularly on weekends.On weekdays, apart from essential commuting or work-related activities, people prefer alternative modes of transportation or staying at home during rainy weather.Consequently, during rainfall, transportation authorities should focus on trafc management near the train station, business districts, and densely populated residential areas to prevent congestion.Simultaneously, attention should be given to taxi dispatching during weekday commuting hours to meet residents' travel needs.

Network Statistical Properties.
In this section, we constructed complex taxi trafc networks under diferent conditions using the methods outlined in Section 4.3.1.We calculated the network attributes for taxi trafc networks on rainy and sunny days during weekdays, weekends, and the entire week.Te computed results are presented in Table 2, where a series of changes articulate the impact of rainfall on taxi trafc networks under various conditions.On rainy weekends, the number of edges decreased from 43,166 to 41,824, representing a reduction of 3.21%.Meanwhile, the number of nodes remained relatively constant, resulting in a decrease in travel connections within the taxi trafc network on rainy days.Changes in the number of network edges afect the average node degree, which signifes the number of links connected to a node in the network, aiding in assessing the connectivity and accessibility of destination nodes in a mobile graph [63].On rainy weekends, the average node degree declined from 62.79 to 59.88, and the node degree variance reduced from 4,271.82 to 3,999.64.Tis indicates a decrease in interactivity within the taxi trafc network during rainfall, with increased heterogeneity in connections between nodes, resulting in an overall reduction in external contacts for taxis.
Additionally, node trafc represents the total volume of trips starting or ending at a node.Te total node trafc and average node trafc on rainy days were both lower than those on sunny days, suggesting that rainfall reduced residents' demand for taxis while leading to a more uneven distribution of trafc fow between nodes, thereby diminishing interactivity.Simultaneously, rainfall caused a slight decrease in the network connectivity of the taxi trafc network, falling below the level observed on sunny days under similar conditions.Te average clustering coefcient, indicative of the degree of clustering among network nodes,    Journal of Advanced Transportation also exhibited a minor decrease.Tis suggests that rainfall led to a reduction in the density of connections between nodes, weakening the clustering connections between taxi road intersections and diminishing the strength of cyclical networks, thereby increasing the probability of node failures (such as trafc congestion or accidents).In summary, across the same time dimensions during weekdays and the entire week, various parameters on rainy days were lower than those on sunny days.Tis implies that rainfall diminishes the cohesion of taxi trafc networks, reducing connectivity and accessibility and potentially leading to trafc congestion or accidents.
In contrast to some biological or technological networks, transportation networks exhibit a pronounced spatial dimension.Figure 9 illustrates the spatial distribution of node degrees on sunny and rainy weekends.Te spatial distribution of node degrees follows a heterogeneous pattern, with high node degree values concentrated in areas with signifcant population mobility, such as train stations and commercial streets, including Hankou Railway Station, Wuchang Railway Station, Jianghan Road Commercial Street, and Optics Valley Square.Simultaneously, as the radial distance from high node degree areas increases, the node degree values experience a slight decline.Temporally, changes in node degrees are not very pronounced, with both sunny and rainy weekends showing higher node degrees in areas like train stations and commercial streets.Minor variations include a subtle increase in node degree at Wuhan Railway Station on rainy weekends and slight decreases near commercial streets and the CBD.By integrating these observations with the documented phenomenon of diminished graph density and heightened average path length during rainfall, as delineated in Table 2, it is evident that the taxi trafc network experiences heightened isolation in local connections on rainy days.Tis could be attributed to the fact that, in the absence of navigation devices at the time, taxi drivers relied on experience to choose routes, and rainfall made route selection more challenging and relatively centralized.

Community Detection and Graph Structure. Community detection in transportation networks is a technique employed to unveil clustering behaviour within the network.
A community can be understood as a set of nodes in the taxi trafc network sharing similar characteristics.Te distinction between internal and external communities is determined by modularity, where a higher modularity value indicates a more reasonable community division with tighter connections among nodes.Conversely, a lower modularity value implies a more ambiguous community division and sparser connections among community nodes.Taxi activities are impacted by rainfall, diminishing the efciency of taxi travel in the network, elevating the probability of trafc congestion, and rendering community delineation more ambiguous.Te modularity decreases from 0.41 to 0.39 over the week, with a more pronounced reduction observed on weekends.Detected community structures are illustrated in Figure 10, with numbers representing distinct community structures.Under diferent weather conditions, four communities on weekends and fve communities on weekdays are identifed, exhibiting similar structures in terms of partition form and geographical coverage.Rainfall induces changes in community structures, causing the expansion of the 1st community on weekends northward, absorbing much of the 2nd community's area (Figure 10(b)).Similarly, rainfall causes the northward expansion of the 1st community on weekdays, albeit to a lesser extent than on weekends.Te 3rd community extends northwestward towards Wuchang Station, and the 5th community is nearly engulfed and merged into the 4th community (Figure 10(d)).Rainfall facilitates community merging, resulting in a reduction in the number of communities and an expansion of geographical coverage.Community merging is somewhat related to node degrees, as residents alter travel destinations during rainfall, reducing high-degree nodes and leading to community transitions.Regions with high node degrees, marked by circles in the fgure, exhibit signifcant community transition phenomena.It can be seen that rainfall broadens the mobility range of taxis, with residents choosing taxis for long-distance travel, thereby increasing the use of medium and long-distance passenger taxis and replacing some of the services normally provided by buses and subways.Compared to weekends, weekdays witness large-scale mobility due to necessary commuting and work-related travel, enlarging community coverage and aligning with the current imbalance in residence and work areas in major cities.

Conclusions
To capture the impact of rainfall on taxi travel patterns and population mobility, this study employed geostatistical analysis and geographic spatial complex network methods to construct a comparative analytical framework for investigating the efects of rainfall on taxi services in Wuhan City at diferent scales.In this research, taxi travel data were utilized to extract passenger trajectory information.Road intersections were designated as nodes, and taxi movements between road intersections served as edges, with the frequency of taxi connections between two road intersections as the weight, thereby constructing a complex taxi trafc network.Te study integrated geostatistical analysis methods and spatial visualization techniques to present the association between rainfall and taxi activities at various scales.Te conclusions are as follows: (1) Rainfall reduced taxi travel volume during diferent time intervals (a 3.96% decrease on weekdays, a 4.46% decrease on weekends, and a 4.16% decrease over the week).However, rainfall increased taxi travel demand during specifc periods (a 4.17% increase between 19: 00 and 22:00 on weekdays).Taxi journeys primarily involve short durations and distances, and rainfall extends residents' travel times, delaying the occurrence of travel peaks.It increased the frequency of short-duration and long-distance trips, a phenomenon more pronounced on weekends.(2) Hotspots for taxi OD points in Wuhan City were concentrated around train stations, CBD areas, commercial streets, Optics Valley Square, and some smaller attractions.Rainfall increased taxi travel in areas near train stations, business districts, and residential areas but decreased travel to leisure tourist spots and commercial pedestrian streets.(3) Rainfall had a greater impact on weekends than on weekdays.It restricted residents' travel range and entertainment activities on weekends, while the large-scale migration on weekdays was mainly due to necessary commuting or work-related activities resulting from a residence-work imbalance.Simultaneously, rainfall altered residents' travel modes to some extent, with more residents opting for taxis during rainy weather.(4) Rainfall expanded the mobility range of taxis, causing changes in community structures.Residents with distant destinations increasingly chose taxis, leading to higher usage rates for mid-to longdistance trips.However, the connectivity and accessibility of the taxi trafc network decreased due to rainfall, resulting in reduced transportation efciency and an increased risk of trafc congestion or accidents.
Te practicality of our multiscale comparative analysis framework has been efectively demonstrated in this study, further afrming the feasibility of taxi trajectory data in the examination of population mobility.Trough our conclusion analysis, we ofer some recommendations for urban policymaking and transportation planning.Firstly, during rainfall, trafc managers should pay attention to trafc guidance at various times near train stations, commercial areas, and densely populated areas, especially during working days, to avoid trafc congestion.Secondly, taxi companies should consider rain-related taxi dispatching.More taxis should be deployed near essential transportation hubs, such as train stations and trafc nodes, during rainy weather.Conversely, the allocation of taxis near scenic spots and entertainment facilities should be reduced on rainy days to ensure residents' travel needs.
Several limitations exist in this study.Firstly, research on big data is constrained by computational performance, demanding signifcant time for data processing.Moreover, this study analysed data for a limited number of days and solely relied on taxi trajectory data to discuss the impact of rainfall on taxi travel patterns and population mobility.Te limited data may weaken the signifcance of the impact of rainfall on population mobility, and a more comprehensive investigation of the efects of rainfall on residents' travel could be achieved by integrating multiple data sources such as smart card transportation data, mobile signalling data, and Weibo check-in data.Secondly, this study focuses solely on the impact of rainfall on population mobility, without considering the infuence of other factors such as temperature, humidity, and wind speed, which can afect residents' travel patterns.Additionally, the psychological impact of prolonged rainy weather in the summer monsoon region is not considered, which is an essential factor infuencing residents' travel.In future research, we can extend the multiscale comparative analysis framework to diferent cities, incorporating various data sources to further investigate the impact of diferent or combined factors on transportation and population mobility patterns.Tis will contribute valuable insights to the universality study of the multiscale comparative analysis framework.

Figure 1 :Figure 2 :
Figure 1: Overview of the study area.(a) Location of the study area in Wuhan City.(b) Study area.

Figure 3 :
Figure 3: Te work fow of our comparative analysis framework.

Figure 4 :
Figure 4: Te relationship between rainfall and travel volume.(a) Sunny and rainy travel volume on weekdays.(b) Sunny and rainy travel volume on weekends.(c) A week of sunny and rainy travel.(d) Te average sunny and rainy travel volume on weekdays and weekends.

Figure 5 :
Figure 5: Travel time-frequency distribution map.(a) Distribution of rainy and sunny weekdays.(b) Distribution of rainy and sunny weekends.

Figure 6 :
Figure 6: Travel distance frequency distribution map.(a) Distribution of rainy and sunny weekdays.(b) Distribution of rainy and sunny

Figure 7 :Figure 8 :
Figure 7: Kernel density distribution of OD points under diferent conditions.(a) O point of rainy weekends.(b) D point of rainy weekends.(c) O point of sunny weekends.(d) D point of sunny weekends.(e) O point of rainy weekdays.(f ) D point of rainy weekdays.(g) O point of sunny weekdays.(h) D point of sunny weekdays.(i) O point of rainy weeks.(j) D point of rainy weeks.(k) O point of sunny weeks.(l) D point of sunny weeks.

Figure 9 :
Figure 9: Spatial distribution of node degree.(a) Sunny rest day.(b) Rainy day of.

Table 1 :
Selection of weather data.

Table 2 :
Comparison of network properties under diferent conditions. (c)