A sensitivity study of the discrete Kalman filter (DKF) to initial condition discrepancies

In several previous studies the discrete Kalman filter (DKF) has been used in an adaptive-iterative mode to deduce time-varying air quality emissions. While it is not expressly stated in previous literature on this method, the DKF assumes that the initial modeled and observed concentrations are equal. Careful consideration of this assumption is critical for urban or regional scale air quality models because agreement of initial concentrations with observations is not always a requirement or priority when using these models. The purpose of this paper is to clarify the initial condition assumption in the DKF and to investigate potential implications when the assumption is violated. We focus on the adaptive-iterative implementation of the DKF since we arc specifically interested in deducing time-varying air quality emissions. A complete description of the adaptive-iterative DKF as implemented by other authors is provided. A case study in the form of a pseudodata test or identical twin experiment is presented to show that if the initial condition assumption is violated, the adaptive-iterative DKF can produce biased emissions to compensate for the initial modeled and observed concentration differences. The magnitude and longevity of the resulting compensating error depends on the influence of the initial concentrations, as the error is removed more quickly for highly reactive species than for less reactive species (e.g., isoprene versus CO).