Formulation of parametric uncertainty forecasts towards operational wildfire smoke assimilation

Operational smoke plume assimilation systems require fast, yet accurate error estimations to represent the large, case-dependent and spatio-temporally varying uncertainties. This study exploits parametric uncertainty forecasts (PUF) as 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. It focuses on (1) the theoretical derivation of forecast dynamics tailored to near-surface air quality applications with uncertain emissions, and (2) the implementation of PM2.5 forecast error standard deviation into the Canadian air quality model GEM-MACH. The theoretical investigation 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, concentration error correlation and correlated emission error, respectively. For illustration purposes, the presented formulation is used for assimilation of surface PM2.5 in an exemplary wildfire case study in eastern Canada in July 2023. Although the setup of the error forecast remains highly simplified, the results show significant differences in hourly PM2.5 analysis increments compared to the operational setup. These differences can be related to the ability of the simple PUF to attribute large analysis increments to highly uncertain areas like wildfire plumes far away from observation locations. Thus, it enables spreading sparse observation information much more efficiently in a highly case-dependent and anisotropic way only though improved variance fields. The presented work leads the way towards efficient operational assimilation for wildfire smoke and other uncertain air quality events using a parametric Kalman Filter (PKF).