Splitting error estimation for micro-physical–multiphase chemical systems in meso-scale air quality models

Operator splitting applied to cloud micro-physical and multiphase chemical process causes the so-called operator splitting errors in addition to other numerical errors when used in numerical models. Operator splitting is mainly used due to limited computer resources or for historical reasons. Unfortunately, it is impossible so far to theoretically estimate either the order of magnitude or the tendency of the splitting errors in complex non-linear systems such as mutually interacting cloud chemical and micro-physical processes. The present study systematically investigates the splitting error mentioned above, by numerical means to define valid ranges of the applicability of the method of operator splitting to those systems. Results of the current study show that de-coupling intervals larger than 100 s cause an underestimation of the total liquid water content as well as the particle radius of the order of 10% for simulation periods of 1000 s. The maximum overprediction of the total content of dissolved material in the particles is of the order of about 20% for de-coupling intervals of 10–15 min. The error in the sulphate production contributes about 50% to the discrepancy in total aerosol content. Since the de-coupling intervals between dynamical, micro-physical, and chemical processes in most recent air quality models are considerably longer than 15 min, the consequences of the application of operator splitting requires further investigation with respect to predicted aerosol formation, cloud water content, deposition rates, photo-chemistry, cloud optical properties, etc.