## 2 Materials and Methods
### Three-Dimensional Air Quality Data Spatial Interpolation Model  
This method aims to transform discrete three-dimensional air quality scattered data into continuous voxel grid data using spatial interpolation techniques, facilitating visualization, analysis, and further scientific research on spatial distribution characteristics. This study utilizes point interpolation to voxel grid technology from SuperMap iDesktop 11i (2022) (V11.0.2) software, which combines advantages of spatial statistics and geographic information systems to effectively address interpolation challenges in three-dimensional spatial data. Each interpolation algorithm in ArcGIS (10.8) software has its own set of strengths and limitations [22]. However, given that the data collected in this experiment consist of non-uniformly distributed three-dimensional scattered points, which are significantly influenced by the geographical characteristics of the microenvironment, the Kriging interpolation method stands out as one of the most robust algorithms for handling such spatially heterogeneous data [23; 24].  
Kriging calculates the weights of known points around unknown points using covariance functions, semivariogram analysis, and theoretical variogram function models, and estimates the attribute values of unknown points through weighted averaging. This method fully considers the three-dimensional distribution characteristics and spatial correlations of data in three-dimensional space, suitable for the interpolation analysis of complex terrain and environmental factors [25].  
Specifically, three-dimensional Kriging interpolation can be described as follows:  
Semivariogram computation: The semivariogram function \(\gamma(h)\) describes the spatial correlation between two points. For three-dimensional data points \((x_{i},y_{i},z_{i})\) and \(\left(x_{j},y_{j},z_{j}\right)\), their distance \(h\) can be expressed as follows [22]:  
\[h=\sqrt{\left(x_{i}-x_{j}\right)^{2}+\left(y_{i}-y_{j}\right)^{2}+\left(z_{i} -z_{j}\right)^{2}} \tag{1}\]  
The semivariogram function \(\gamma(h)\) typically employs empirical formulas or theoretical models such as exponential, Gaussian, or spherical models.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Specification** \\ \hline \multirow{4}{*}{Receiver type} & channel u-blox M9 engine \\  & GPS L1 C/A, QZSS L1 C/A/S, GLONAS L10F \\  & BeiDou B1I, Galileo E1B/C \\  & SBAS L1 C/A:WAAS, EGNOS, MSAS, GAGAN \\ \hline \multirow{2}{*}{Nav. update rate} & Up to 25 Hz (4 concurrent GNSS) \\ \hline \multirow{2}{*}{Horizontal position accuracy} & 1.5 m CEP (with SBAS) \\  & 2.0 m CEP (without SBAS) \\ \hline \end{tabular}
\end{table}
Table 3: Specifications of the Holybro M9N GPS for velocity measurements in the x, y, and z directions.  
Covariance function and variogram model: Based on the semivariogram function, the covariance function \(C(h)\) and variogram model are constructed to define the spatial relationship between known and unknown points.  
Kriging coefficients are computed by solving the Kriging coefficient matrix equation, which determines the weight \(\lambda_{i}\) for each known point. For a target point \((x_{0},y_{0},z_{0})\), the estimated attribute value \(t_{0}\) can be expressed as follows:  
\[t_{0}=\sum\limits_{i=1}^{n}\lambda_{i}t_{i} \tag{2}\]  
where \(t_{i}\) represents the attribute value of the known point \((x_{i},y_{i},z_{i})\), and \(\lambda_{i}\) denotes the corresponding weight coefficient, determined by the following system of linear equations:  
\[\left\{\begin{array}{ll}\sum\limits_{i=1}^{n}\lambda_{i}\gamma\big{(}(x_{i}, y_{i},z_{i}),\big{(}x_{j},y_{j},z_{j}\big{)}\big{)}+\mu=\gamma\big{(}(x_{0},y_{0},z_{0}), \big{(}x_{j},y_{j},z_{j}\big{)}\big{)},\ \ j=1,2,\ldots,n\\ \sum\limits_{i=1}^{n}\lambda_{i}=1\end{array}\right. \tag{3}\]  
where \(\mu\) is the Lagrange multiplier used to ensure that the sum of the weight coefficients equals 1.  
This study interpolates three-dimensional air quality scattered data with 60 interpolation layers, each layer accurate to 1 m.