Development and impact of weak-constraint 4DVar with model bias consideration in the CMA-GFS

The standard strong-constraint four-dimensional variational data assimilation (SC-4DVar) approach was designed to correct random, zero-mean errors in both model forecasts and observations in the China Meteorological Administration Global Forecast System (CMA-GFS). However, global numerical weather prediction (NWP) models often exhibit significant systematic biases within the assimilation windows. To address this limitation, a weak-constraint 4DVar (WC-4DVar) approach, which explicitly accounts for model biases, has been proposed as a method for reducing the impact of these biases. In this study, the WC-4DVar approach is integrated into the CMA-GFS, and a one-month cycling assimilation and forecasting experiment is conducted to evaluate its effectiveness. The WC-4DVar approach incorporates a model bias term into the cost function, with the control variables and covariance matrix estimated from 240 samples collected over a one-year period from the CMA ensemble data assimilation (EDA) trial. The results show that WC-4DVar significantly reduces the model biases, particularly in regions with larger biases. Specifically, the analysis fields are improved, as evidenced by the negative root-mean-squared error reduction ratios obtained for the temperature and wind components. WC-4DVar exhibits an enhanced ability to forecast the geopotential height, temperature, and wind fields in the northern hemisphere within the first 192 hours. In the southern hemisphere, significant enhancements are observed in the upper atmosphere during the first 96 hours. Additionally, WC-4DVar improves its forecasting ability at the top of the model in tropical regions. These findings highlight the potential of WC-4DVar to serve as a valuable tool for improving operational NWP systems, particularly in regions where systematic biases are most pronounced.