Physical and numerical contributions to the structure of Kelvin wave-CISK modes in a spectral transform model

Nonlinear Kelvin wave-CISK modes'' are critically assessed as a possible mechanism for the Madden-Julian Oscillation (MJO) with a global spectral transform model and a one-dimensional analog. Convection is parametrized using a simple ``positive-only CISK'' scheme, where tropospheric diabatic heating is proportional to the low-level convergence, and is set to zero in regions of low-level divergence. Although the modes have many properties that are consistent with the MJO, they also have a serious drawback. The growth rate of unstable modes depends crucially on the width of the heating region, which is resolution dependent. The ``CISK catastrophe'' has not been averted, and the heating region collapses to the smallest localized scale that the model can support. This scale is larger than the model resolution, as measured by both the gridpoint-scale and the inverse wavenumber or half-zonal-wavelength of the highest wavenumber basis function, and is associated with the appearance of negative Gibbs fringes which are then cut off by the positive-only CISK parametrization.