In geosciences, data assimilation (DA) combines modeled dynamics and observations to reduce simulation uncertainties. Uncertainties can be dynamically and effectively estimated in ensemble DA methods. With respect to current techniques, the novel Gauss-Hermite High-Order Sampling Hybrid filter (GHOSH) ensemble DA scheme is designed to improve accuracy by reaching a higher approximation order, without increasing computational costs, as demonstrated in idealized Lorenz96 tests.