Resolving aerosol dynamical processes in the sub-10 nm range is crucial for our understanding of the contribution of new particle formation to the global cloud condensation nuclei budget or air pollution. Accurate measurements of the particle size distribution in this size-range are challenging due to high diffusional losses and low charging and/or detection efficiencies. Several instruments have been developed in recent years in order to access the sub-10 nm particle size distribution; however, no single instrument can provide high counting statistics, low systematic uncertainties and high size-resolution at the same time. Here we compare several data inversion approaches that allow combining data from different sizing instruments during the inversion and provide python/Julia packages for free usage of the methods. We find that Tikhonov regularization using the L-curve method for optimal regularization parameter estimation gives very reliable results over a wide range of tested data sets and clearly improves standard inversion approaches. Kalman Filtering or regularization using a Poisson likelihood can be powerful tools, especially for well-defined chamber experiments or data from mobility spectrometers only, respectively. Nullspace optimization and non-linear iterative regression are clearly inferior compared to the aforementioned methods. We show that with regularization we can reconstruct the size-distribution measured by up to 4 different mobility particle size spectrometer systems and several particle counters for datasets from Hyytiälä and Helsinki, Finland, revealing the sub-10 nm aerosol dynamics in more detail compared to a single instrument assessment.

解析亚 10 nm 范围内的气溶胶动力学过程对于我们理解新粒子形成对全球云凝结核预算或空气污染的贡献至关重要。由于高扩散损失和低充电和/或检测效率，在该尺寸范围内准确测量粒度分布具有挑战性。近年来开发了多种仪器以获取亚 10 nm 的粒度分布；然而，没有一种仪器可以同时提供高计数统计数据、低系统不确定性和高尺寸分辨率。在这里，我们比较了几种数据反演方法，这些方法允许在反演期间组合来自不同大小工具的数据，并提供免费使用这些方法的 python/Julia 包。我们发现使用 L 曲线方法进行最优正则化参数估计的 Tikhonov 正则化在广泛的测试数据集上给出了非常可靠的结果，并明显改进了标准反演方法。卡尔曼滤波或使用泊松似然的正则化可以是强大的工具，特别是对于明确定义的腔室实验或仅分别来自迁移谱仪的数据。与上述方法相比，零空间优化和非线性迭代回归明显较差。我们表明，通过正则化，我们可以重建由多达 4 个不同迁移率粒度光谱仪系统和几个粒子计数器测量的尺寸分布，用于来自芬兰海蒂拉和赫尔辛基的数据集，