A new operational ocean reanalysis system (ORAS4) has been implemented at ECMWF. It spans the period 1958 to the present. This article describes its main components and evaluates its quality. The adequacy of ORAS4 for the initialization of seasonal forecasts is discussed, along with the robustness of some prominent climate signals.ORAS4 has been evaluated using different metrics, including comparison with observed ocean currents, RAPID-derived transports, sea-level gauges, and GRACEderived bottom pressure. Compared to a control ocean model simulation, ORAS4 improves the fit to observations, the interannual variability, and seasonal forecast skill. Some problems have been identified, such as the underestimation of meridional overturning at 26 • N, the magnitude of which is shown to be sensitive to the treatment of the coastal observations. ORAS4 shows a clear and robust shallowing trend of the Pacific Equatorial thermocline. It also shows a clear and robust nonlinear trend in the 0-700 m ocean heat content, consistent with other observational estimates. Some aspects of these climate signals are sensitive to the choice of sea-surface temperature product and the specification of the observation-error variances. The global sea-level trend is consistent with the altimeter estimate, but the partition into volume and mass variations is more debatable, as inferred by discrepancies in the trend between ORAS4-and GRACE-derived bottom pressure.

This article describes the implementation of an incremental first guess at an appropriate time three‐dimensional variational (3DVAR) data assimilation scheme, NEMOVAR, in the Met Office's operational 1/4 degree global ocean model. NEMOVAR assimilates observations of sea‐surface temperature (SST), sea‐surface height (SSH), in situ temperature and salinity profiles and sea ice concentration. The Met Office is the first centre to implement NEMOVAR at 1/4 degree and the required developments are discussed, with particular focus on the specification of the background‐error covariances. Background‐error correlations in NEMOVAR are modelled using a diffusion operator. The horizontal background‐error correlations for temperature, salinity and sea ice concentration are parametrized using the Rossby radius, which produces relatively short correlation length‐scales at mid to high latitudes, while a flow‐dependent mixed‐layer depth parametrization is used to define the vertical length‐scales for the 3D variables. Results from a one‐year reanalysis with NEMOVAR are presented and compared with the preceding operational data assimilation scheme at the Met Office. NEMOVAR is shown to provide significant improvements to SST, SSH and sea ice concentration fields, with the largest improvements seen in regions of high variability such as eddy shedding and frontal regions and the marginal ice zone. This improvement is associated with shorter correlation length‐scales in the extratropics and an improved fit to observations in NEMOVAR. Some degradation to subsurface temperature and salinity fields where data are sparse is identified and this will be the focus of future improvements to the system.

No abstract

An important element of a data assimilation system is the statistical model used for representing the correlations of background error. This paper describes a practical algorithm that can be used to model a large class of two-and three-dimensional, univariate correlation functions on the sphere. Application of the algorithm involves a numerical integration of a generalized diffusion-type equation (GDE). The GDE is formed by replacing the Laplacian operator in the classical diffusion equation by a polynomial in the Laplacian. The integral solution of the GDE defines, after appropriate normalization, a correlation operator on the sphere. The kernel of the correlation operator is an isotropic correlation function. The free parameters controlling the shape and lengthscale of the correlation function are the products K~T , p = 1,2, . . . , where ( -1 ) p~~ is a weighting ('diffusion') coefficient ( K~ > 0) attached to the Laplacian with exponent p , and T is the total integration 'time'. For the classical diffusion equation (a special case of the GDE with K~ = 0 for all p > 1) the correlation function is shown to be well approximated by a Gaussian with length-scale equal to ( 2~1 T)'/'.The Laplacian-based correlation model is particularly well suited for Ocean models as it can be easily generalized to account for complex boundaries imposed by coastlines. Furthermore, a one-dimensional analogue of the GDE can be used to model a family of vertical correlation functions, which in combination with the twodimensional GDE forms the basis of a three-dimensional, (generally) non-separable correlation model. Generalizations to account for anisotropic correlations are also possible by stretching andor rotating the computational coordinates via a 'diffusion' tensor. Examples are presented from a variational assimilation system currently under development for the OPA Ocean general-circulation model of the Laboratoire d'Octanographie Dynamique et de Climatologie.

SUMMARYIt is common in meteorological applications of variational assimilation to specify the error covariances of the model background state implicitly via a transformation from model space where variables are highly correlated to a control space where variables can be considered to be approximately uncorrelated. An important part of this transformation is a balance operator which effectively establishes the multivariate component of the error covariances. The use of this technique in ocean data assimilation is less common. This paper describes a balance operator that can be used in a variable transformation for oceanographic applications of three-and fourdimensional variational assimilation. The proposed balance operator has been implemented in an incremental variational data assimilation system for a global ocean general-circulation model. Evidence that the balance operator can explain a significant percentage of background-error variance is presented. The multivariate analysis structures implied by the balance operator are illustrated using single-observation experiments.

No abstract

No abstract

Incremental four-dimensional variational assimilation (4D-Var) is an algorithm that approximately solves a nonlinear minimization problem by solving a sequence of linearized (quadratic) minimization problems of the formwhere x is the control vector, A is a symmetric positive-definite matrix, b is a vector containing data and prior information, and c is a constant. This paper proposes a family of limited-memory preconditioners (LMPs) for accelerating the convergence of conjugate-gradient (CG) methods used to solve quadratic minimization problems such as those encountered in incremental 4D-Var. The family is constructed from a set of vectors {s i : i = 1, . . . , l}, where each s i is assumed to be conjugate with respect to the (Hessian) matrix A. In incremental 4D-Var, approximate LMPs from this family can be built using conjugate vectors generated during the CG minimization on previous outer iterations. The spectral and quasi-Newton LMPs employed in many operational 4D-Var systems are shown to be special cases of the family of LMPs proposed here. In addition, a new LMP based on Ritz vectors (approximate eigenvectors) is derived. The Ritz LMP can be interpreted as a stabilized version of the spectral LMP. Numerical experiments performed with a realistic global ocean 4D-Var system are presented, to test the impact of the three different preconditioners. The Ritz LMP is shown to be more effective than, or at least as effective as, the spectral and quasi-Newton LMPs in our 4D-Var experiments. Our experiments also demonstrate the importance of limiting the number of CG (inner) iterations on certain outer iterations to avoid possible divergence of the cost function on the outer loop. The optimal number of CG iterations will depend on the specific preconditioner used, and can be computed a priori, albeit at the expense of several evaluations of the cost function on the outer loop. In a cycled 4D-Var system, it may be necessary to perform this computation periodically to account for changes in the Hessian matrix arising from changes in the observing system and background-flow field.