The initial state for a geophysical numerical model is produced by combining observational data with numerical model simulation using a data assimilation algorithm. Particularly challenging is the application of these algorithms in weather forecasting at the storm and convective scale. For these applications, high resolution nonlinear numerical models are used. In addition, intermittent convection is present in the simulations and observations, often leading to errors in locations and intensity. In addition, the state vector has a large size, one third of which contains variables whose non-negativity needs to be preserved, and the estimation of the state vector has to be done frequently in order to catch fast changing convection. Finally, often, not only one, but rather an ensemble of predictions is needed in order to correctly specify, for example, the uncertainty of rain at a particular location, even further increasing the computational considerations.
In current practice, many data assimilation methods do not preserve the non-negativity of variables and rely on Gaussian assumptions. We present an algorithm that could be used for weather forecasting at the convective scale, that is based on the ensemble Kalman filter (EnKF) and quadratic programming. This algorithm outperforms the EnKF as well as the EnKF with the lognormal change of variables for all ensemble sizes. For a model that was designed to mimic the important characteristics of convective motion, preserving non-negativity of rain and conserving mass reduce the error in all fields; they prevent the data assimilation algorithm from producing artificial mass or artificial rain. Finally, important reduction in the computational costs has been recently achieved, making it possible to apply this algorithm in high dimensional weather forecasting problems in the future.