Integrating Global Parameter Estimation into the Weakly Constrained Local Ensemble Transform Kalman Filter for Convective-Scale Data Assimilation

Ensemble Kalman filters often violate physical conservation laws due to their underlying assumptions, particularly affecting non-negative variables like hydrometeors in convective-scale data assimilation. To address this issue, we develop an enhanced weakly constrained local ensemble transform Kalman filter (WCLETKF) that incorporates an online estimation method for global conservation parameters. This approach augments the state vector to treat conservation references as jointly estimated global parameters, using a tailored tapering scheme to simultaneously enforce constraints and update the model state without relying on imperfect background estimates or unknown truth. The method is evaluated by using twin experiments with an idealized 1D shallow water model configured for total rain mass conservation. Results demonstrate that the proposed framework, which estimates constraints online, outperforms both the standard LETKF and the weakly constrained version WCLETKF that uses background-derived references. It achieves superior analysis accuracy for wind, height, and rain variables, reduces rain mass bias, and enhances short-term forecast skills. Moreover, due to the coupling effect of the variable field, a positive effect has also been achieved in terms of the conservation of total energy. This study establishes a foundation for integrating generalized conservation laws into ensemble-based assimilation systems and highlights promising future directions, including extension to other filters and validation in high-dimensional, realistic convective-scale models.