In this paper, the authors present Plume Rise Iterative Stratified Moist (PRISM),  an update to the Briggs model which considers the moist thermodynamics of rising plumes. The choice of the Briggs model makes sense because the authors are interested in stack plumes (rather than wildfire smoke plumes for which Freitas would be more suitable). This paper is well written and the introduction clearly communicates why moist thermodynamics is important for stack plumes. In my opinion the paper does a good job comparing PRISM with the previous layered version of Briggs that did not consider water vapor. I was particularly convinced by the confidence ratios. Also, it makes the important point that the PRISM model is sensitive to stack water emissions and that implementing PRISM substantially reduces bias.

This paper starts to lose me when the authors talk about whether GM-orig or GM-PRISM is better at predicting plume top heights, as the authors do not use stack water emissions to drive these models. Lack of data is a totally normal issue, but due to the fact that the PRISM model was so sensitive to stack water emissions, with stack water emissions impacting plume top heights by up to 500m, I am not sure that the bias reduction given by GM-PRISM is as big as the authors report it to be. If stack water is added and GM-PRISM heights go up closer to GM-orig, than the bias reduction might be much smaller.

Therefore, I am recommending the following major revisions.

1. I would recommend that the authors look at observed plume heights for the test cases where they do have water emissions. It looks like for the offline model simulations, stack water emissions were used, could observed plume heights be reported here as well? This would go a long way to convincing me that the bias correction is as large as reported in the current version of the paper.

2. In section 2.1, there seems to be a lot of overlap with the supplement, and the main text and the supplement seem to present the overlapping material in a slightly different order. For instance, line 117-118 says “derivations of the formulae presented here are provided in the supplement” but by this point Equation (1) has been presented, the derivation of which is shown in Supplement S1 Eq1-Eq6. I would recommend making sure that supplement equations are referenced where relevant in the main text, and I would perhaps make it more clear that the supplement is using the discrete forms of the model equations and the main text is using the continuous forms.

3. Throughout the methods and results section, I would suggest that the authors are more clear in differentiating the offline PRISM vs the GM-PRISM. I would make sure the offline and online simulations are mentioned in the intro and section 2.2 and 2.6. It might also make sense to reorganize the methods as follows (using current section numbers): 2.1, 2.2, 2.6, 2.4, 2.3, 2.5.

4. The authors might want to consider a title which indicates that this paper is about developing a new model. That way it could reach the audience of people who might want to apply this model.

5. It might be nice to combine figures 4 and 5, since they have a lot of the same information. I liked the format of Fig 5 and the error bars in Fig 4.

Overall, nice work and I look forward to seeing a revised version.

This study introduces a new approach (PRISM - Plume-Rise-Iterative-Stratified-Moist) for modeling how industrial smoke plumes rise and spread in the atmosphere, with a special focus on how water content affects plume behavior. The water vapor condensation and evaporation were often overlooked in previous models but shown to be crucial for plume rise dynamics. This study makes a valuable contribution to air quality modeling by demonstrating the importance of including water vapor effects in plume rise calculations, with scientific ground evidence from both theoretical analysis and observational comparisons. Overall, the paper is well written, and the model experiments are well structured. I recommend the publication of this paper and have a few minor suggestions.

1. The authors have mentioned about two different plume rises (“vertical” and “bent-over”) in section 3.1 and different formulations for these two types in section 2.1. Maybe it is obvious for the authors, but I think it worths a brief explanation of their differences to benefit broader audience.
2. The choice of density convergence criteria (r_conv) may be critical in determining the final plume height. Is it scientifically rigorous enough to conclude that including water content improves plume rise predictions when this conclusion is based on simulations using ρconv = 0.3%, a value chosen because it produced better matches with observations? Based on the sensitivity studies on different values of r_conv shown in Table S1 and S2, it is difficult to conclude that GM-PRISM performs better than GM-orig. I suggest the authors to provide more scientific justification for the r_conv = 0.3% selection.
3. I assume Fig. 5 and 6 are showing overlapping information, is it correct? Why not combine these two figures and show them at the same time and altitude scales like Fig. 6 but with the error bars like Fig. 5?
4. It is very difficult to compare the bias and see the station IDs in Fig. 7b and 7d. Is it possible to show in other formats such as bar chart?