A non-Gaussian ensemble filter for assimilating infrequent noisy observations

We present a modified ensemble Kalman filter that allows a non-Gaussian background error distribution. Using a distribution that decays more slowly than a Gaussian allows the filter to make a larger correction to the background state in cases where it deviates significantly from the truth. For high-dimensional systems, this approach can be used locally. We compare this non-Gaussian filter to its Gaussian counterpart (with multiplicative variance inflation) with the three-dimensional Lorenz-63 model, the 40-dimensional Lorenz-96 model, and Molteni's SPEEDY model, a global model with ∼10⁵ state variables. When observations are sufficiently infrequent and noisy, the non-Gaussian filter yields a significant improvement in analysis and forecast errors.