Hydrometeor background errors in convective systems are strongly non-Gaussian because of zero inflation, truncation, and vertical microphysical stratification, which can degrade the optimality and stability of variational data assimilation. This study develops a layer-adaptive Gaussian transformation for hydrometeor control variables and implements its forward, inverse, tangent linear, and adjoint operators in an operational variational assimilation system. Offline diagnostics for an extreme precipitation case in South China show that the proposed transformation preserves the inherent spatial structures of hydrometeor fields while maintaining meaningful statistical properties, reducing non-Gaussianity by 74%–93% across five hydrometeor species. Operational variational assimilation experiments show that the proposed method improves convergence stability, increases the departure reduction index from 73.8% to 86.7%, and generates hydrometeor increments with more coherent physical structures and closer agreement with ERA5 reference fields. These results indicate that physically informed Gaussian transformation provides a practical pathway for improving hydrometeor analysis in variational assimilation without relying on discontinuous zero-value treatments.

Gaussian transformation; hydrometeor assimilation