| 30 Dec 2025
Towards a parametric Kalman filter for operational wildfire plume assimilation: Formulation of the forecast step
Abstract. This study introduces a simple parametric Kalman Filter (PKF) specifically tailored to the requirements of operational air quality data assimilation under highly uncertain emissions like wildfire smoke events. Operational smoke plume assimilation systems require fast, yet accurate error estimations to represent the large, case-dependent and spatio-temporally varying uncertainties. The PKF offers a computationally efficient alternative to existing ensemble approaches, where the dynamics of error parameters (such as error standard deviations) are explicitly evolved numerically at a fraction of the cost of ensemble-based methods. This study focuses on the forecast step of the PKF by evolving error standard deviations in the Canadian operational air quality model GEM-MACH. It includes the following three steps: 1) theoretical derivation of forecast dynamics tailored to near-surface air quality applications with uncertain emissions, 2) implementation into the GEM-MACH modeling system, 3) application to surface PM2.5 in eastern Canada during a wildfire episode in July 2023.
The theoretical investigation conducted in this study suggests that error standard deviation is a more suitable parameter than error variance for operational models. This is due to improved process-understanding, numerical accuracy, and a simpler form of the forecast equation that can be implemented with minor modifications of the forecasting model. Implementing diffusion and emission processes of errors in a state-of-the-science atmospheric model for the first-time demonstrates their sensitivity to other error parameters, state error correlation and emission error, respectively. Although the setup of the error forecast remains highly simplified, the case study results show significant impacts on hourly PM2.5 analysis increments compared to the operational setup. These 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. Thus, spreading sparse observation information much more efficiently in a highly case-dependent and anisotropic way only though improved variance fields.
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.