Forecast Skill and Computational Cost of the Correlation Models in 3DVAR Data Assimilation

Many background error correlation (BEC) models in data assimilation are formulated in terms of a positive-definite smoothing operator B which simulates the action of correlation matrix on a vector in state space. To estimate the efficiency of such approach, numerical experiments with the Gaussian and spline models have been conducted. Here I is the identity operator and nu is the diffusion tensor, whose spatial variability is derived from the forecast field and m is the spline approximation order. Performance of these BEC representations are compared in the framework of numerical experiments with real 3dVar data assimilation into the Navy Coastal Ocean model (NCOM) in the Western Tropical Pacific. It is shown that both BEC models have similar forecast skills over a two-month time period, whereas the second-order spline model is several times more efficient computationally if the cost function is minimized in the state space.
Published in Atmospheric Science and Ocean Sciences, Advances in Geosciences, v28, p1-14, 2012.