The numerical stability of a parametrization of convective momentum transport

The Gregory et al. parametrization of momentum transport by convection is s hown to be more prone to numerical instability than other parts of the conv ection scheme, because of an additional element of numerical diffusion. The limiting Courant number for Linear stability is (1 + c)(-1), where c is th e parameter which controls the dependence of the pressure gradient on envir onmental shear. Some revised numerical treatments cure the instability prob lem but reduce forecast skill, apparently because the diffusive element of the original formulation is beneficial, even though it is artificial. A pos sible solution to the problem is to use an implicit treatment of the origin al formulation which is absolutely stable.