The impact of a balance constraint between temperature and humidity on the global humidity analysis in GRAPES

In order to improve the humidity analysis in GRAPES global three dimensional variational data assimilation system (GRAPES-3DVar), a statistical balance constraint between temperature and humidity has been introduced into the formulation of background error covariance based on the previous work by Hólm et al. (2002).By deducting the balanced part associated with temperature and using a nonlinear normalization method, the normalized unbalanced pseudo-relative humidity is used as the new humidity control variable. Statistical results show that the coupling between temperature and humidity is related to large scale upwelling and condensation and mainly appears in areas where the environmental relative humidity is larger than 80%. Such areas are often found in the middle troposphere over mid-and high-latitudes. The results also show that the new humidity control variable is nearly unbiased with a Gaussian distribution pattern of error characteristics. Experiments of single pseudo-observation show that the analysis is flow-dependent and the problem of negative moisture and super-saturation is less severe by using the new humidity analysis scheme. Results of cycle analysis and forecast experiments indicate that the bias and root mean square error of the humidity analysis both decrease. The precipitation verification results show that, for the 0.1-10 mm precipitation forecast at 24 hour interval, the Equitable threat score (ETS) changes little, but the bias score (BIAS) is much closer to 1 and the false alarm rate decreases. However, the miss rate for heavy rainfall (> 25 mm) in the 60-84 hour forecast has increased, which means the humidity analysis needs further improvement in the future. This study improves GRAPES 3DVAR by introducing the statistical balance constraint between temperature and humidity into the system, which has laid a solid foundation for continuous improvements of the global humidity analysis in the future.