Background Error Covariance Matrix Structure and Impact in a Regional Tropical Cyclone Forecasting System

The background error covariance matrix (BE) is a fundamental component of data assimilation (DA) systems. Its impact on both the DA process and subsequent forecast performance depends on model configuration and the types of observations assimilated. However, few studies have specifically examined BE behavior in the context of satellite DA for regional tropical cyclone (TC) prediction. In this study, we develop the BE and evaluate its structure for a TC forecasting system over the western North Pacific. A total of six BEs are modeled using three control variable (CV) schemes (aligned with the CV5, CV6, and CV7 options available in the Weather Research and Forecasting DA system (WRFDA)) with training data from two distinct periods: the TC season and the winter season. Results demonstrate that the BE structure is sensitive to the training data used. The performance of TC-season BEs derived from different CV schemes is assessed for TC track forecasting through the assimilation of microwave sounder satellite brightness temperature data. The evaluation is based on a set of 14 cases from 2018 that exhibited large official track forecast errors. The CV7 BE, which uses the x- and y-direction wind components as CVs, captures finer small-scale momentum error features and yields greater forecast improvement at shorter lead-times (24 h). In contrast, the CV6 BE, which employs stream function (ψ) and unbalanced velocity potential (χu) as CVs, incorporates more large-scale momentum error information. The inherent multivariate couplings among analysis variables in this scheme also allow for closer fits to satellite microwave brightness temperature data, which is particularly crucial for forecasting TCs that primarily develop over oceans where conventional observations are scarce. Consequently, it enhances the large-scale environmental field more effectively and delivers superior forecast skill at longer lead times (48 h and 72 h).