Multivariate assimilation in MERCATOR project: New statistical parameters from forecast error estimation

Abstract

The new operational prototype of Mercator (french Global Ocean Data Assimilation Experiment contribution) is composed of a North Atlantic primitive equation ocean model OPA (Ocean Parallel Algorithm between 20°S and 70°N, [Madec, G., P. Delecluse, M. Imbard and C. Lévy (1998). OPA8.1 ocean general circulation model reference manuel. Notes du pôle de modélisation IPSL. n°11: 91p]) and of a multivariate and multidata assimilation scheme [De Mey, P. and M. Benkiran (2002). “A multivariate reduced-order optimal interpolation method and its application in Mediterranean basin-scale circulation.” Ocean Forecasting : Conceptual basis and application, Pinardi, N., Springer Verlag.] This system has already given some significant improvements from previous Mercator configurations (M. Benkiran, personal communication). However some biases on ocean state still remain in the tropics where the reduced-order optimal interpolation scheme is suspected to be ill-parameted in the model forecast error. Indeed the guess error covariance matrix is decomposed into an error variance value and a spatio-temporal correlation function which are assumed to have some “good” properties (spatial homogeneity of the correlation function, constant ratio between signal and error variance). This study shows how we can use ensemble methods to validate these assumptions. We can see that the correlation function can reach negative values locally, mostly in regions of high variability contradictory with the homogeneous hypothesis. The reduced space used in the operational configuration is based on the signal seasonal Empirical Orthogonal Functions (EOFs). An empirical relationship between signal and error variance has been set and the correlation function is the same on every dimension of the reduced space. By projection of the estimated guess error variance onto the reduced space, we find a repartition of this quantity quite different to what was set in the system. The error statistics is found to be inhomogeneous compared to hypothesis made in the assimilation scheme. These two new parameters tested separately in the assimilation scheme gives significant improvements of the forecast and analysis results. This is particularly obvious in the tropics. But relationship between signal and error statistics (as assumed in the optimal interpolation) is found to be complex.