Believable Scales and Parameterizations in a Spectral Transform Model

Through analysis of the spectra of a Dirac delta function the notion of believable and unbelievable scales in a spectral transform model is quantified. The smallest resolved local features are shown to have an average wavenumber a factor of 2 less than that of the truncation, and a half-width 1.6 times greater than that associated with the smallest-scale waves and 2.4 times the maximum grid size of a quadratic transform grid. A reassessment of the philosophy of including parameterizations is introduced, the central point of which is a separation of the parameterization and dynamical truncation scales. The use of spectral filters applied to the input and output from gridpoint physical parameterization schemes and the use of a coarse “physics” grid are proposed. Diagnostics summarizing the noise in a spectral model are introduced, and a moist baroclinic wave life-cycle simulation and a one-dimensional analog to photochemistry at the terminator are discussed to demonstrate their use.