Contour-advective semi-Lagrangian algorithms for many-layer primitive equation models

For an f-plane many-layer primitive-equation isopycnal model, three 'contour-advective semi-Lagrangian' (CASL) algorithms and a standard pseudo-spectral (PS) algorithm are compared as regards their representation of balance and imbalance during the evolution of a highly complex vortical flow with substantial activity in small horizontal and vertical scales. The three CASL algorithms employ (q, h, delta), (q, delta, gamma), and (q, gamma, Xi) as their prognostic variables, where q is the Rossby potential vorticity, h is layer thickness, 6 is horizontal divergence, gamma and Xi represent departures of vorticity from, respectively, geostrophic and Bolin-Charney balance. It is demonstrated that the CASL algorithm with (q, delta, gamma) improves on the algorithm with (q, h, delta) across nearly the whole range of applicability of the algorithms, i.e. practically up to the limit where overturning and diabatic effects may dominate. Unlike in the PS algorithm, the improvement is achieved without sacrificing the accuracy of the vortical part of the flow by excessive damping.