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the Creative Commons Attribution 4.0 License.
| 22 Jul 2025
Evolution of Aerosol Particle Number Size Distribution in Statistical Thermodynamic Equilibrium During New Particle Formation and Growth
Abstract. The aerosol particle number size distribution (PNSD) is pivotal in estimating the corresponding transport, transformation, environmental impacts, and climate effects. This study explores the statistical thermodynamic characteristics of PNSD during new particle formation (NPF) and growth in clean atmospheric environments. Using the maximum entropy principle, we demonstrate that the PNSD follows the Weibull distribution of n(Dp) = N0Dpq−1 e−αDpq (q is the shape parameter). Field observation and theoretical analysis show that q would evolve from above 6 to 3 during different stages of NPF due to the various strengths of condensation, indicating that the aerosol is in the statistical thermodynamic equilibrium state. The findings provide insights into the underlying physical mechanisms governing aerosol behavior and have implications for model simulations of aerosol evolution.
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RC1: 'Comment on egusphere-2025-3012', Anonymous Referee #1, 21 Aug 2025
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This manuscript investigates the usability of the Weibull distribution (WD) in representing atmospheric aerosol number size distributions undergoing simultaneous new particle formation (NPF) and particle condensation growth. The investigation includes a theoretical part, in which specific forms of WD are derived under different boundary layer conditions, and then these distributions are applied to ambient measurement data. While the theoretical part of the work is of scientific interest, its applicability to aerosol number size distributions in real atmospheric situation appear vague, especially what it comes to some of the made assumptions and interpretations. My main criticism in this regard are summarized below.
First, all of the used quantities and concepts should be explained in the paper. What is the scale parameter alfa in eq. 2? What exactly is meant by the aerosol assumed to be in statistical equilibrium? What is meant by coagulation ratio (line 147)?
Second, the statement on line 81 is incorrect. The total aerosol mass concentration is constant only when there is no condensation at all. If the purpose is to say that mass concentration can be approximated constant when condensation is weak enough, then some concrete way of quantifying whether this approximation is valid should be explicitly given when deriving eq. 6.
Third, the derivation of equations is done by assuming a clean atmosphere, by which the authors apparently mean that coagulation of newly formed and growing particle into the background aerosol particle population can be neglected. In most atmospheric environments this is rarely the case over the time scales of interest. For example, in the case shown in Fig. 1 the time scale by which newly formed particles coagulation with the background particle population is comparable to (or slightly larger than) the inverse of CS, i.e. typically less than a minute. This means that coagulation cannot be neglected over the times of interest in the chosen case.
Fourth, the non-validity of WD during the initial stages of NPF is explained by rapidly changing particle number concentration, although the important quantity for eq. 6 is the change in aerosol mass concentration. I would argue that the invalidity of eq. 6 during the initial stages of NPF is due to growth of newly formed particle (changing the total particle mass concentration) rather by having more particles in the system.
Finally, the behavior of q in Fig. 4d makes the applicability (and interpretation) of WD to this case questionable. In defining the different stages of NPF and growth (lines 103-120), the authors state that q could be initially larger than 5 but then it should decrease from 5 to 3. What is the interpretation of values below 3 over long time periods in Figure 4? No explanation is given how these periods fit the sequence of stages defined on lines 103-120. Also, condensation effects should become negligible when q approaches 3. By comparing Figs. 4a and 4d, q is close to 3 even when particle clearly grow in size. i.e. when condensation evidently influences the particle number size distribution.
Taken together, the paper is unable to demonstrate that WD is applicable to real situations of NPF and growth in the atmosphere, as both significant condensation and coagulation influence the particle number size distribution over most of the time. The assumptions made in the paper, and especially in defining the different stages of NPF and growth, might be better valid under laboratory experiments investigating NPF, in which the background aerosol population may be truly negligible and where condensable vapors can really be depleted during the experiment. As a result, I cannot recommend accepting this paper for publication in Atmospheric Chemistry and Physics. With suitable revisions addressing the points highlighted above, the paper might be suitable for publication is some other journal (e.g. in specific aerosol journals dealing with laboratory experiments on NPF and growth).
Citation: https://doi.org/10.5194/egusphere-2025-3012-RC1
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