Development of the Adjoint-free 4dVar Technique for Regional Models

The advent of massively parallel computers accelerated the development of ensemble methods of data assimilation and their synthesis with the variational techniques. Of particular interest are the approaches which do not require tangent linear numerical models and their adjoints for optimization. These ``adjoint-free'' methods minimize the cost function within the subspace spanned by perturbations of the control variables, derived from a given ensemble. In this presentation, we explore an adjoint-free variational technique (a4dVar) which does not require an external ensemble. Minimization of the cost function is performed a sequence of subspaces generated in the process of optimization.

Performance of the method is assessed in two regional configurations of ocean models: the Navy Coastal Ocean Model (NCOM), and the surface wave model (Wavewatch III). With the NCOM, both adjoint and adjoint-free 4dVar data assimilation techniques are compared in application to the hydrographic surveys and velocity observations collected in the Adriatic Sea. Numerical experiments have shown that a4dVar is capable of providing forecast skill similar to that of conventional 4dVar at comparable computational expense while being less susceptible to excitation of ageostrophic modes that are not supported by observations. The a4dVar technique constrained by the Wavewatch III model is tested in a series of data assimilation experiments with synthetic observations in the southern Chukchi Sea. The types of considered observations are directional spectra estimated from point measurements by stationary buoys, significant wave height (SWH) observations by coastal high-frequency radars and along-track SWH observations by satellites. The a4dVar forecast skill is shown to be 30-40\% better than the skill of the sequential assimilation method based on optimal interpolation which is currently used in operations.

Prospects of further development of the a4dVar method in regional applications are discussed.