An improved calculation of Coriolis terms on the C grid

The central differencing grid with fully staggered velocity components(C grid) is widely used in primitive equations oceanographic models despite potential problems in simulating baroclinic inertiagravity and Rossby waves that can arise due to the averaging of velocity components in the Coriolis terms. This note proposes a new averaging of the velocity components in order to calculate the Coriolis terms on the C grid. The averaging weights are calculated from the minimum of a suitably defined cost function which optimally minimizes the error in the inertial part of frequencies of inertia-gravity waves and maintains the second order accuracy of the computations. The theoretical analysis of wave frequency diagrams shows that the new scheme results in more accurate frequencies of long inertia-gravity and Rossby waves, especially when the Rossby radius of deformation is not resolved well by the grid resolution