This manuscript developed a series of theoretical derivation for background error standard deviation (BESD) from processes including advection, vertical diffusion, point emission etc. These dynamic BESD has case-dependent and anisotropic features. There are two major issues in this manuscript. The theoretical derivation used some assumptions, like “assuming concentration errors at emission locations to be highly correlated to local emission errors” (line 661). This assumed condition is usually valid only for short-lived species emitted from isolated point sources, such as SO2 or NOx from power plants. Applying this assumption to wildfire aerosols needs some justifications, considering that PM2.5 aerosols are relatively long-lived species and the impact of upstream emissions could be significant, especial for the forest fires where the fire spots are usually adjacent. Other important factors, such as fire plume rises, were not mentioned. The changed BESD should also affect the assimilation in elevated layers, but this study and discussion are limited in surface PM2.5 only, without touching anything about aerosol optical depth, an important wildfire plume indicator. Another issue is that this manuscript lacks observation-based verification, and study period is too short. The case study application (section 4) only shows the one-day BESD and analysis increment (June 06, 2023), compared with the operational setup. There is no evaluation using observations.

Here are some specific comments.

Section 2.1. For the advection of error field, how to consider the wind field error? This derivation assumes no error on meteorological field. However, in real situation, this error should exist.

Section 2.2 The vertical diffusion of errors only consider the simplest K-theory diffusion. For big wildfire, the plume rise and convection could be the major factor affecting the pollutant’s vertical distribution.

Section 2.3 As the wildfire spots are usually adjacent, the simple assumption of local emission determining local PM2.5 concentrations could have issues.

Section 3.1 Insufficient detail on model configuration (e.g., resolution, chemistry scheme, boundary conditions, emissions treatment).

Section 4. The case study is only limited to one-day event, and there is no direct evaluation against observations.

General comments:

This study presents a simple parametric Kalman Filter (PKF) specifically tailored to the requirements of operational air quality data data assimilation under highly uncertain emission like wildfire smoke events. The study focuses on the forecast step of the PKF by evolving error standard deviations in the Canadian operational air quality model GEM-MACH. The results of a case study during a wildfire episode in July 2023 in eastern Canada show the simple PKF can significantly impact the hourly PM2.5 analysis increments compared to the operational setup. The differences can be related to the ability of the simple PKF to attribute large analysis increments to highly uncertain areas like wildfire plumes far away from observation locations. However, the study is limited to only one case study of one day.

Major comments:

1. How much uncertainty is the used wildfire emissions from CFFEPS for the case study? Is it consistent with the estimated uncertainty proposed with the linear relation between emissions and concentrations in section 3.3?
2. It is better to firstly give a figure shown the wildfire emissions for the studied case. Where and when the wirdfire hoppen during the studied case?
3. It is sugguested to add the meteorological fields in Figure 2 to see how the emitted PM2.5 from the wirdfire are transported.
4. In section 4.3, it is recommended to quantitative evaluation of the analysis increments with assimilated observations of the two experiments to see whether the PKF is superior to the operional one.
5. In section 4.3, the analysis increments like wildfire plumes far away from observation locations could be evaluated with satellite observed optical properties.