Implementation of a Balance Operator in NCOM

Abstract : The balance operator and its adjoint for the Navy Coastal Ocean Model (NCOM) have been coded. The operator is implemented in two modes: (a) with and (b) without the integral continuity constraint. Testing the code in an Adriatic Sea configuration has shown that although the a-mode option is several times more computationally expensive, it provides half the ageostrophic motions excited by perturbations with a typical horizontal scale of the internal Rossby radius of deformation. For a state vector of 1.5M degrees of freedom, the total CPU time required by the code is negligible compared to the CPU time required by 1 hour of NCOM integration (i.e., 15 and 80 times less for the a- and b-mode options, respectively). The code could be used in the design of the background error covariance operators in both variational and ensemble applications of data assimilation.