## 4 Methodology
### Regional Indicators of Urban Freight Mobility  
In this study, we constructed a series of regional indicators based on urban freight activities at the grid level to measure the functional positioning of regional freight. Their definitions are as follows. Related Trip Volume (\(T\)): The sum of the number of trips whose origins or destinations are located within a specific grid. As a core indicator reflecting the freight attractiveness and generation of an area, the related trip volume provides a fundamental dimension of scale for identifying urban freight functional zones. It serves as a crucial basis for delineating freight \"hotspots\" and an important reference for optimizing resource allocation. Given the extreme imbalance in the distribution of trip volumes, we employed the logarithm of related trip volumes to mitigate the impact of data skewness, calculated as follows:  
\[T=log_{10}(T_{o}+T_{d}), \tag{1}\]  
where \(T_{o}\) and \(T_{d}\) represent the number of origin and destination trips in a specific grid, respectively. Daily Trip Volatility (\(V\)): This indicator is designed to quantify the fluctuation of the daily related trip volume within a grid. By measuring the dispersion of daily trip, it accurately reveals the stability and dynamic patterns of regional freight activities. Daily trip volatility is measure through the coefficient of variation (CV), calculated as follows:  
\[V=\frac{\sigma(T)}{\mu(T)}\times 100\%, \tag{2}\]  
Figure 3: Demonstration of study area, with a few key freight infrastructures listed. where \(\mu(T)\) and \(\sigma(T)\) represent the mean and standard deviation of related trip volume for a specific grid over \(n\) days. Vehicle Type Entropy (\(E_{T}\)): Vehicle type entropy measures the distribution of trips across vehicle categories within a grid, serving as a core indicator to quantify the specialization level of freight activities. By applying information entropy theory, this indicator evaluates the evenness of trip distribution across vehicle types, revealing the structural characteristics of regional freight functions. A low \(E_{T}\) value represents a more specialized freight zone while a high \(E_{T}\) value represents one with a more diversified distribution. \(E_{T}\) is calculated as follows:  
\[N=\sum_{i=1}^{n}N_{i}, \tag{3}\]  
\[E^{\prime}_{T}=-\sum_{i=1}^{n}\frac{N_{i}}{N}\cdot log_{2}\bigg{(}\frac{N_{i} }{N}\bigg{)} \tag{4}\]  
\[E_{T}=\frac{E^{\prime}_{T}}{log_{2}n} \tag{5}\]  
where \(N_{i}\) represents the trip count of the \(i\)-th vehicle type (only vehicle types with more than two trips are retained to enhance calculation robustness, with fewer trips treated as sporadic data), \(n\) denotes the number of valid vehicle types, \(N\) is the total number of trips associated with valid vehicle types, \(E^{\prime}_{T}\) is the raw entropy value, and \(E_{T}\) is the normalized vehicle type entropy (used to eliminate variations caused by differing trip volumes across grids). Vehicle ID Entropy (\(E_{I}\)): Vehicle ID entropy measures the distribution of trips across different vehicles within a grid, serving as a core indicator to characterize the operational model of regional freight activities. By quantifying the evenness of trip distribution across vehicle IDs through information entropy, this indicator reveals principal operational models and acts as an important basis for evaluating the efficiency and stability of regional freight organization. A low \(E_{I}\) value demonstrates a fleet-based operation while a high value demonstrates an individual-based operation. \(E_{I}\) is calculated as follows:  
\[\overline{M}=\frac{1}{m}\sum_{i=1}^{m}M_{i}, \tag{6}\]  
\[M^{\prime}_{i}=\left\{ \begin{array}{l}M_{i}^{2},\ \textit{when}\ M_{i}\geq 2.\overline{M}\\ M_{i},\ \textit{when}\ M_{i}<2.\overline{M}\end{array} \right.