Balance constraints for the background error covariance of aerosol species and applications for CalNex experiment

The background error covariance (BEC) is important in data assimilation to spread information between different variables and produce balance analysis fields. The BEC spreads information between different variables to produce balanced analysis fields by employing balance constraints to convert original variables into new independent variables. Using statistical regression, we develop a balance constraint for the BEC of aerosol variables and apply it to a three-dimensional variational data assimilation system in the WRF/Chem model. One-month forecasts from the WRF/Chem model are employed for BEC statistics. The cross-correlations between the different species are generally high. The largest correlation occurs between elemental carbon and organic carbon with as large as 0.9. After using the balance constraints, the correlations between the unbalanced variables reduce to less than 0.2. A set of data assimilation and forecasting experiments is performed. In these experiments, surface PM2.5 concentrations and speciated concentrations along aircraft flight tracks are assimilated. The analysis increments with the balance constraints show spatial distributions more complex than those without the balance constraints, which is a consequence of the spreading of observation information across variables due to the balance constraints. The forecast skills with the balance constraints show substantial and durable improvements compared with the forecast skills without the balance constraints.