2023 was record-breaking for wildfires in Canada with unprecedented impacts on local ecosystems as well as large scale smoke hazards. Fire smoke plumes are extreme air quality events with exceptionally high concentrations and related uncertainties fall outside statistical ranges. These particular conditions induce specific challenges for data assimilation algorithms, because error estimates need to represent the high uncertainties and spatial gradients. A novel assimilation approach, called parametric Kalman filter (PKF), explicitly propagates the main error parameters in a forecast model to create reasonable uncertainty estimates at very low computational costs. Similar to atmospheric constituents, the accuracy of forecasting error parameters relies on the physical processes that are considered. As a first step, the most important processes to be considered in a variance forecast for fire aerosols are investigated in this case study. It is shown that a variance source term which represents the uncertainties in emissions, vertical diffusion and advection are critical processes for dynamical variance simulation during extreme air quality events. This provides an important step towards parametric aerosol assimilation for improved wildfire smoke forecasts in the operational forecast model GEM-MACH.