General Comments

This paper presents a method called the optimized incremental random forest ensemble forecasting model with the localized ensemble Kalman filter (OIRF-LEnKF), which combines an computationally lightweight emulator of PM2.5 chemical components with the efficient and accurate data assimilation method LEnKF. This paper also presents a mechanism for online learning to update the OIRF model as new data arrives. The results on a real-world assimilation task of PM2.5 concentrations in a region in China show that the proposed algorithm is effective in remaining stable across a long assimilation horizon while effectively assimilating observations that lead the analyses to remain close to a notion of ground truth (based on reanalysis). The use of machine learning in various data assimilation applications is an important investigation, however, the authors could provide more motivation for particular choices made while creating the OIRF-LEnKF algorithm and perhaps further contextualize this work in relation to related work. 

Scientific Comments

A - The authors propose a random forest model that is incrementally optimized as new information about the system is obtained, but provides minimal motivation for the choice of random forest over other approaches. This application area involves spatial datasets, which make a neural network architecture like a CNN a good fit, especially given that many state-of-the-art emulators of spatial systems rely in part on CNNs. The motivation for the choice of RF should be made more clear in the paper, and perhaps an ablation against a CNN-type architecture should be provided. To create an ensemble like a random forest, the CNN training could be bagged.

B - Have there been other successful ML models of PM2.5 chemical components? If so, they should be cited in the related work. If these emulators do exist, why were any of them not used instead of the authors' proposed random forest model?

C - In line 90, a claim is made that increasing the number of ensemble members in the forecast “mitigates the underestimation of forecast error covariance”. It certainly helps mitigate, but it is not an assured cure. The authors should modify the language to something like “helps mitigate” to make the statement more accurate.

D - Is the idea of throwing away decision trees that do not perform as well as a predefined threshold on the updated dataset a novel contribution of this paper, or has this approach been used elsewhere? If it has been used elsewhere, the previous works should be cited.

Technical Corrections

A - It would be helpful to spell out the name of the OIRF-LEnKF in the abstract (line 15).

B - In line 55, “DA technique has been widely used [...]” should be corrected to either “DA has been widely used [...]” or “DA techniques have been widely used [...].”

C - “Where” immediately after equation (1) should be lowercase.

D - What criteria is used to determine a split for each decision tree? Is it based on MAE? This should be made more clear in the text (roughly around line 145).

E - y is used to describe an analysis in line 154 but is then used to describe observations in line 215. The authors should stay consistent in the text that y refers to observations.

F - In lines 154-155, should “nth grid point after DA” be changed to the “ith grid point”? And similarly should “nth DT at the nth grid point” be changed to “nth DT at the ith grid point”?

G - Immediately after equation (5), it should be made clear that f_t^{DT}(x,theta_n) with a bar over the expression refers to the ensemble mean across decision trees in the random forest.

H - I think that the paper would benefit from a mathematical formulation of the difference between domain localization and observation localization (in the section in lines 219-243).

I - The construction of W in equation (11) is not immediately clear. What values do i and j range from? Why is this matrix forced to be diagonal? What is the dimensionality of W? The answers to these questions should be made more clear in the text.

J - In Table 1, could the authors please also list the dimensions of the analysis (# latitudes, # longitudes, # features)? 

K - In Figure 3a, is the objective referenced from the Bayesian optimization? It may be more clear to reference an equation number in the caption. In Figure 3c, why is there a sudden decrease at an ensemble size of 30 in the OIRF-LEnKF/NP2 (%)?

L - The colorbar in all subfigures in Figure 4 should start at 0 so that perceived color variations more closely correspond to significant differences in the values in the table. Figure 4c, for example, has two different colors assigned to 0.77 in the bottom right corner, likely due to small differences past the third decimal place. If these heatmaps no longer look interesting after making this change, then another plotting technique highlighting any interesting aspects should replace Figure 4.

Please find the attached report.