Modelling of ambient particle number concentrations (PNC) has been implemented in the Danish air quality modelling system DEHM/UBM/AirGIS and evaluated with long-term measurements. We implemented particle dynamical processes in the regional scale model DEHM using the M7 aerosol dynamics module (presented in the accompanying article by Frohn et al. 2021), and we developed models for PNC at the local scale (UBM) and street scale (OSPM), in a first approximation without including the particle dynamics as presented in this article.

Outdoor concentration estimates are provided at the front door of all residential address locations in Denmark for the past 40 years (1979 – 2018) with a spatial resolution of 1 km x 1 km taking all emission sectors in Denmark into account and additionally at the street location, with significant traffic (> 500 vehicles / day).

We evaluated our model with up to 18-year long measurement time series of particle number size distributions (PNSD) at Danish street, urban and rural background stations. Two particle size ranges were used for evaluation: PNC_>10 (count of particles with diameter larger than 10 nm) and PNC_{30_250} (diameter range 30 to 250 nm), in order to exclude nucleation events from the measurements and to obtain a consistent long-term measured time series.

When comparing our model estimates with PNC_{30_250} measurements, we obtain Pearson correlation coefficients (R_p) in the range 0.39-0.95 depending on station location (street, urban background, rural) and averaging time (hour, day, month, year). The highest correlations were found for yearly averages at a monitoring station located at a street with dense traffic (R_p=0.95) whereas shorter time averages and comparisons with monitoring stations at urban and rural background locations provided lower correlations. The model performance for PNC in terms of correlation coefficients with respect to measurements is comparable to the performance for other pollutants such as NO_X , PM_2.5 and better than the performance for PM₁₀.

The model generally overestimated the observed concentrations, Normalised Mean Bias (NMB) was in the range 6% to 190% compared to PNC_>10 and 90% to 290% compared to PNC_{30_250}. These relatively high NMBs are probably caused by uncertainties in the modelling process, especially the estimation of particle number emissions, which largely determine the ambient concentrations of PNC. Furthermore, uncertainties might as well originate from the complexity of modelling particle dynamical processes accurately and the great challenges in performing long-term PNC measurements.

The presented model can estimate PNC at all Danish addresses over the last 40 years with a 1-hour time resolution. The data seem to provide a good indication of the relative differences in PNC at Danish addresses.

丹麦空气质量建模系统 DEHM/UBM/AirGIS 已对环境粒子数浓度 (PNC) 进行建模，并通过长期测量进行评估。我们使用 M7 气溶胶动力学模块（在 Frohn 等人于 2021 年发表的随附文章中介绍）在区域尺度模型 DEHM 中实现了粒子动力学过程，并且我们开发了局部尺度 (UBM) 和街道尺度 (OSPM) 的 PNC 模型，在不包括本文中介绍的粒子动力学的情况下的第一个近似值。

过去 40 年（1979 年至 2018 年）在丹麦所有住宅地址位置的前门提供室外浓度估计值，空间分辨率为 1 公里 x 1 公里，同时考虑了丹麦的所有排放部门以及街道位置, 交通量大（> 500 辆车/天）。

我们使用丹麦街道、城市和农村背景站长达 18 年的颗粒数粒度分布 (PNSD) 测量时间序列评估了我们的模型。使用两个粒径范围进行评估：PNC _{> 10}（直径大于 10 nm 的颗粒计数）和 PNC _{30_250}（直径范围 30 至 250 nm），以便从测量中排除成核事件并获得一致的长-term 测量的时间序列。

将我们的模型估计值与 PNC _{30_250}测量值进行比较时，我们根据站点位置（街道、城市背景、农村）和平均时间（小时、天、月、年）获得了范围为 0.39-0.95 的Pearson 相关系数 (R _p )。位于交通密集的街道上的监测站的年平均值具有最高的相关性 (R _p = 0.95)，而较短的时间平均值以及与城市和农村背景位置的监测站的比较提供了较低的相关性。PNC 模型在测量相关系数方面的性能与其他污染物（如 NO _X、PM _2.5）的性能相当并且优于 PM ₁₀的性能。

该模型通常高估了观察到的浓度，归一化平均偏差 (NMB) 与 PNC _{> 10}相比在 6% 至 190% 的范围内，与 PNC _{30_250}相比在 90% 至 290%_之间。这些相对较高的 NMB 可能是由建模过程中的不确定性引起的，尤其是粒子数排放的估计，这在很大程度上决定了 PNC 的环境浓度。此外，不确定性也可能源于精确建模粒子动力学过程的复杂性以及执行长期 PNC 测量的巨大挑战。

所提出的模型可以估计过去 40 年来所有丹麦地址的 PNC，时间分辨率为 1 小时。数据似乎很好地表明了丹麦地址 PNC 的相对差异。