Weakly Constrained LETKF for Estimation of Hydrometeor Variables in Convective-Scale Data Assimilation

The ensemble Kalman filter algorithm can produce negative values for non-negative variables. To mitigate this sign problem and to simultaneously maintain the mass conservation, a new concept of combining weak constraints on mass conservation and non-negativity has been introduced in this work, with a focus on hydrometeor variables in convective-scale data assimilation. We modify the local ensemble transform Kalman filter with weak constraints on mass conservation for each hydrometeor variable and adopt the assimilation of clear-air reflectivity data as a weak constraint on non-negativity. We examine the concept by a series of sensitivity experiments using an idealized setup. Results show that both weak constraints successfully improve the mass conservation property in analyses and both reduce the biased increase in integrated mass-flux divergence and vorticity. Furthermore, the least biased increase is obtained by combining both constraints, and the best forecasts are also achieved by the combination.