Abstract Ultrafine particles (UFP) pose a risk to human health, but due to the multitude of sources and fast transformation in the urban atmosphere, quantifying the exposure is challenging. Furthermore, physical properties of aerosol particles depend on the particle size. Statistical models are used to quantify spatial and temporal variation of UFP, but rarely used for particle number size distribution (PNSD). The aim of the study was to establish an interpretable statistical model capturing spatial and temporal variation of urban PNSDs using generalized additive models (GAM) and multivariate adaptive regression spline models (MARS). These algorithms automatically fit interpretable, non-linear marginal function to represent relationships between explanatory and response variables. Three different approaches were evaluated to cope with the multidimensionality of the PNSD data (20–800 nm, 34 size bins): a generalized additive model for the particle number concentration (PNC) of every individual size bin (GAMbins), a generalized additive model for the parameters of the PNSD function (GAMpams) and a multivariate adaptive regression spline model for the PNC of every size bin (MARSbins). Reanalysis data of meteorological quantities, urban geometry parameters and approximated traffic counts were used as explanatory variables. Marginal functions of the final models could be attributed to major processes that contribute to spatial and temporal variation of the PNSD, i.e. emissions from vehicle traffic, transport, dilution, accumulation, deposition and new particle formation. Cross-validation coefficients of determination ranged between 0.27 and 0.48 for most size bins. Nonetheless, the modelling approaches resulted in similar root mean square errors (RMSE) and mean absolute error (MAE). Though direct spatial transferability of the models is limited, the presented approaches may be useful for estimating ambient exposure to particles.

中文翻译：

---

交通和背景站点城市粒子数大小分布时空变化的统计建模

摘要 超细颗粒 (UFP) 对人类健康构成威胁，但由于来源众多且城市大气中的快速变化，量化暴露具有挑战性。此外，气溶胶颗粒的物理特性取决于颗粒尺寸。统计模型用于量化 UFP 的空间和时间变化，但很少用于粒子数大小分布 (PNSD)。该研究的目的是建立一个可解释的统计模型，使用广义加性模型 (GAM) 和多元自适应回归样条模型 (MARS) 来捕捉城市 PNSD 的空间和时间变化。这些算法自动拟合可解释的非线性边际函数来表示解释变量和响应变量之间的关系。评估了三种不同的方法来处理 PNSD 数据的多维性（20-800 nm，34 个尺寸箱）：每个单独尺寸箱 (GAMbins) 的粒子数浓度 (PNC) 的广义加法模型，广义加法模型用于 PNSD 函数 (GAMpams) 的参数和用于每个大小箱 (MARSbins) 的 PNC 的多元自适应回归样条模型。气象量、城市几何参数和近似交通计数的再分析数据被用作解释变量。最终模型的边际函数可归因于导致 PNSD 空间和时间变化的主要过程，即来自车辆交通、运输、稀释、积累、沉积和新颗粒形成的排放。对于大多数大小箱，交叉验证确定系数范围在 0.27 和 0.48 之间。尽管如此，建模方法导致了相似的均方根误差 (RMSE) 和平均绝对误差 (MAE)。尽管模型的直接空间可转移性有限，但所提出的方法可能有助于估计环境对粒子的暴露。