Based on a comprehensive dataset of field observation, Li et al. developed a series of J-models to better predict aerosol formation rates globally. In the models, sulfuric acid (SA) was considered the dominant gaseous nucleation precursor, and RH was used to represent the meteorological impacts of NPF. Overall, the models' performance was satisfactory and showed significant improvements over the SA-Organic binary nucleation model. It is well-accepted that aerosols play an important but extremely uncertain role in regulating the solar-terrestrial radiation budget. It is still very challenging for climate models to accurately predict PNSD and aerosol number concentration on a global scale due to the complexity and diversity of nucleation mechanisms worldwide. Therefore, this is a very important work although the parameterization method were compromised by data availability and the possibility of over-fitting. It is difficult to use one set of parameters to estimate NPF rates worldwide. The limitations of these models should be fully addressed. Therefore, I would recommend this manuscript for publication after the following comments are sufficiently addressed.

Specific comments:

1) L217-218: I think the correction for hygroscopic growth was necessary for the intercomparisons. The CS and CoagS terms may vary substantially depending on the RH and the aerosol chemical compositions.

2)L248: It is understandable not to include HOMs and NH3 in the parameterization due to the lack of data. However, it is more important to know how the exclusion of these compounds would impact the performance of these models. How sensitive are these models to the H2SO4 data, especially when H2SO4 proxies are used, which may lead to substantial uncertainty in H2SO4 input data?

3) L356: Strictly speaking, NPFs were often associated with Low RH conditions, which does not necessarily mean that low RH favors NPFs. These two phenomena may concur due to the same underlying cause. For instance, stronger solar irradiation can lead to higher ambient temperature and, thus, lower RH. However, the real factor in intensifying NPF could be the increased atmospheric photooxidation capacity that led to more production of NPF gas precursors.

4) L357: It is a bit strange that the higher SA and lower CS in Värriö would lead to a lower frequency of NPF.

5) L373: There is still no direct evidence that meteorology will significantly impact NPF in Beijing. The CS term was indeed playing a critical role in regulating NPF in Beijing.

6) L374-375: How did background aerosols sustain NPF? Did not the loss to preexisting aerosols compete with the formation of sub-5 nm particles? The high levels of background SO2, VOCs, and their oxidation products may be responsible for the intense NPFs in Beijing.

7) L411: These results strongly suggested that precursors other than H2SO4 should be considered for these models to work appropriately in marine environments.

8) L426: The Manacapuru case may be very special. The RH was very high year-round, and thus, J5 became insensitive to variations in RH and the corresponding aerosol hygroscopic growth, which may be treated as a constant. This may explain the better slope (1.02) found in model 1 simulation (Fig. 3h1).

9) These J-models were developed to predict NPF rates globally, but they did not consider nucleation mechanisms involving iodine oxoacids (IO). Since ~70% of the Earth's surface is seawater, how would this affect the application of these J-models by omitting IO-related NPF mechanisms?

Xinyang Li and colleagues present four different parametrization models for predicting the formation rates of 5 nm particles (J₅). These models utilize measurements of sulfuric acid, particle number size distribution, and meteorological variables such as relative humidity from six diverse locations worldwide.

The models also incorporate condensation sink and coefficients describing nucleation activation, survival efficiency, and cluster stability. The authors found that including both relative humidity and condensation sink alongside sulfuric acid significantly improves the accuracy of J₅ predictions across all six places. Since these locations span boreal forest, rural, urban, and marine environments, they suggest that models 3 and 4 can be applied on a global scale.

Additionally, the authors used their models to calculate particle size number distributions, demonstrating that, particularly for Aitken particles, their approach outperforms the Riccobono model.

By relying on readily available data, this parametrization offers a practical tool for broader atmospheric modeling. Given these contributions, I recommend this manuscript for publication after addressing the following comments.

Comments:

Sulfuric acid proxy data, and in line 225. The reference from Dada is provided, but are the calculations shown for these datasets mentioned anywhere in the manuscript or supplementary material?

Line 218. What would be the effect of considering the correction for hygroscopic growth?

Line 222. The detection limit of H₂SO₄ is exceptionally good at 5 × 10³ molecules per cubic centimeter. Was this case for all the mass spectrometers considered here?

Can the authors clarify how low RH and NPF are related? It is not entirely clear to me. Similarly, I do not fully understand how this phenomenon can be seen on Figure 3 as indicated in lines 355-357.

I understand the lack of data availability for HOMs and NH₃. However, when describing NPF in polluted environments, NH₃ is essential. Do you think an NH₃ proxy can be used in the future? How might the results change if NH₃ were included? Could you also comment on how the addition of ammonia will influence the model, and especially which coefficients will be influenced by that and why? I would be very interested in hearing your thoughts on this.

Lines 249-250. Please add more references, particularly when discussing not only ammonia but also HNO₃. The authors could mention, for example, the synergetic NPF mechanism including sulfuric acid + ammonia + nitric acid.

Lines 319-321. What do the authors think could be a potential mechanism for NPF in Budapest during spring, as supported by results described in Section 4.1.2?

Lines 398-400. Which marine vapors could improve the performance of the model? Additionally, in lines 405-406, could the author indicate which vapors are expected to influence NPF, along with relevant references?