Estimation and Impact of Nonuniform Horizontal Correlation Length Scales for Global Ocean Physical Analyses

Abstract

Optimally modeling background-error horizontal correlations is crucial in ocean data assimilation. This paper investigates the impact of releasing the assumption of uniform background-error correlations in a global ocean variational analysis system. Spatially varying horizontal correlations are introduced in the recursive filter operator, which is used for modeling horizontal covariances in the Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC) analysis system. The horizontal correlation length scales (HCLSs) were defined on the full three-dimensional model space and computed from both a dataset of monthly anomalies with respect to the monthly climatology and through the so-called National Meteorological Center (NMC) method. Different formulas for estimating the correlation length scale are also discussed and applied to the two forecast error datasets. The new formulation is tested within a 12-yr period (2000–11) in the ½° resolution system. The comparison with the data assimilation system using uniform background-error horizontal correlations indicates the superiority of the former, especially in eddy-dominated areas. Verification skill scores report a significant reduction of RMSE, and the use of nonuniform length scales improves the representation of the eddy kinetic energy at midlatitudes, suggesting that uniform, latitude, or Rossby radius-dependent formulations are insufficient to represent the geographical variations of the background-error correlations. Furthermore, a small tuning of the globally uniform value of the length scale was found to have a small impact on the analysis system. The use of either anomalies or NMC-derived correlation length scales also has a marginal effect with respect to the use of nonuniform HCLSs. On the other hand, the application of overestimated length scales has proved to be detrimental to the analysis system in all areas and for all parameters.