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.