Traditional urban zoning methods primarily focus on the spatial distribution of urban functions, neglecting the temporal dynamics of urban space usage. As urban density increases, multiple functions often coexist within the same space, leading to complex human activity patterns. For example, a space might be a workplace during the day, a restaurant at noon, and an entertainment venue at night. Understanding these temporal patterns – the daily rhythm of urban space usage – is crucial for effective urban management and planning. Previous studies have employed various data sources, including remote sensing, field observations, and human-tracking data (mobile phone data, GPS data, etc.) to classify urban spaces into functional zones. However, these studies mostly focus on spatial heterogeneity, overlooking the temporal dynamics. This paper addresses this gap by investigating the daily rhythm of urban space usage in Beijing, China, a city characterized by high urban density and diverse urban functions. The study aims to identify distinct daily usage patterns and analyze how the distribution and combination of urban functions influence these patterns. The findings are expected to provide valuable insights for fine-grained urban decision-making processes.

Existing urban zoning methods predominantly rely on spatial distributions of land use and functions, initially utilizing field observations or remote sensing to classify urban areas. The advent of big data has enabled the use of human-tracking data (GPS, mobile phone data, social media) to delineate functional zones based on spatio-temporal activity characteristics. Studies have categorized urban areas into residential, business, commercial, and open space zones using clustering methods applied to mobile phone data or transit card data. While these studies provide insights into spatial heterogeneity, they often overlook the temporal dynamics of urban space usage. The literature also explores the theories behind urban function distribution, such as Central Place Theory, Neo-Classical Location Theory, New Economic Geography, and Urban Ecology, which provide insights into human mobility patterns. However, existing research often neglects the complex interplay between multiple coexisting urban functions and their impact on daily usage rhythms at a fine-grained temporal scale (e.g., hour-by-hour). This study aims to bridge this gap by focusing on the temporal heterogeneity of urban space usage, considering the interactive effects of coexisting urban functions.

The study area encompassed areas within the fifth ring road of Beijing, divided into 10,889 grid cells (250 x 250 m). Point-of-Interest (POI) data from Baidu Maps (August 2017) provided information on urban functions within each grid cell, categorized into enterprises, entertainment, residences, schools, healthcare facilities, government buildings, shops, restaurants, parks, and tourism establishments. Mobile signaling data (MSD) from China Unicom, covering five weekdays (January 9-13, 2017), were used as a proxy for human mobility. The MSD, initially containing unique user IDs, timestamps, and locations, were aggregated to the grid cell level, resulting in approximately 6.8 million trips. Trips shorter than 30 minutes were filtered out. The average number of destinations per hour in each grid cell was calculated, forming a 24 x 10,889 time-space matrix. The k-means algorithm, after data normalization, was employed to cluster the grid cells based on their hourly destination counts, identifying seven distinct daily usage rhythms. Multinomial logistic (MNL) models, using Stata 16.0, were then built to investigate how the distribution and combinations of urban functions influenced these daily rhythms. The dependent variable was the seven daily usage rhythm types, with low equilibrium serving as the reference category. Independent variables included the number of facilities for each urban function and interaction terms between pairs of urban functions. Model diagnostics, including Variance Inflation Factor (VIF) checks, were performed to address potential multicollinearity issues. The significance of the models was evaluated using the chi-square test, and goodness of fit was assessed using log likelihood, AIC, BIC, and McFadden's R². Finally, a validation study was conducted in three typical zones (Wangjing, Sanlitun, and Shichahai) to illustrate the findings.

The k-means clustering yielded seven distinct daily rhythm types: high equilibrium, low equilibrium, diurnal, nocturnal, morning, evening, and noon-type. These patterns were spatially mapped, revealing distinct geographical distributions. High equilibrium, diurnal, morning, and noon-type zones were concentrated in core urban areas, while evening and low equilibrium zones were predominantly located on the periphery. The MNL model results indicated significant relationships between urban functions and daily usage rhythms. Working functions were associated with high equilibrium, diurnal, and morning rhythms. Residing functions were associated with high equilibrium, diurnal, nocturnal, and evening rhythms. Catering functions were related to high equilibrium, diurnal, morning, evening, and noon rhythms. Healthcare functions were associated with high equilibrium, diurnal, nocturnal, morning, and noon rhythms. Entertainment functions were associated with high equilibrium, diurnal, nocturnal, and evening rhythms. Education functions were linked to high equilibrium, diurnal, and morning rhythms. Shopping functions were associated with high equilibrium, diurnal, and evening rhythms. Touring functions were associated with high equilibrium, diurnal, morning, evening, and noon rhythms. The analysis also highlighted the interactive effects of coexisting functions. Some functions (working, residing, healthcare, education, touring) played dominant roles when coexisting with others, while others (catering) often acted as accompanying functions. The validation study in Wangjing, Sanlitun, and Shichahai zones supported the model findings, demonstrating the diverse interplay between urban functions and daily usage rhythms in different areas.

The study's findings address the research question by identifying distinct daily rhythms of urban space usage and demonstrating their relationship with urban function distribution and combinations. The results underscore the importance of considering temporal dynamics in urban planning and management. The identification of dominant and accompanying functions when functions coexist provides valuable insights for integrating and coordinating different urban functions to enhance efficiency and synergy. The spatially distinct distributions of daily usage rhythms highlight the need for localized interventions tailored to specific temporal patterns and functional mixes. The study's significance lies in its contribution to fine-grained urban analysis and its implications for optimizing resource allocation, improving urban livability, and facilitating time-sensitive planning and provision of infrastructure and services.

This study identified seven distinct daily rhythms of urban space usage in Beijing, revealing a strong relationship between these rhythms and the distribution and interaction of urban functions. The findings highlight the limitations of traditional spatial-only urban zoning and emphasize the need for a more nuanced approach that incorporates temporal dynamics. Future research could explore the daily rhythms of urban space usage in other cities with varying densities and functional mixes. Further investigation into the relationship between daily rhythms and other factors, such as socioeconomic characteristics and transportation modes, could also provide valuable insights for more effective urban planning and management.

The study used data from a specific period (five weekdays in January 2017) in Beijing, limiting the generalizability of the findings to other cities or time periods. The reliance on mobile signaling data as a proxy for human activity may introduce biases, as mobile phone usage patterns may not fully reflect the activities of the entire population. The MNL model, while comprehensive, may not capture all the complexities of the interactions between urban functions and daily usage rhythms. Finally, while the study acknowledges potential endogeneity issues, further investigation using advanced econometric techniques could strengthen causal inference.