A comparison of various normal-mode initialization schemes and the inclusion of diabatic processes

Abstract

The field changes produced by various normal mode initialization schemes are compared. Dynamically balanced data are obtained from a climate simulation using a forecast model. The data are first degraded by a linear initialization, and then a nonlinear initialization is used in an attempt to recover the original fields. The nonlinear initializations include both diabatic and adiabatic schemes, applied to various sets of modes defined using both equivalent depths and natural periods as criteria. Results indicate that diabatic initialization improves specification of the meridional mass streamfunction (i.e., the zonal wavenumber zero Hadley circulation) compared with adiabatic initialization. However, for zonally varying fields, the difference is less dramatic. An exception occurs when shallow modes are initialized, in which case near-surface fields are better specified using diabatic initialization. Errors in the tropical divergent wind field are typically half their true value, for either diabatic or adiabatic initializations. For vertical modes 1–2, errors in specification of mode coefficients are typically less than 20% of their true r.m.s. values. For shallower modes whose natural periods are less than one day, these errors are greater than 40%, but for those longer period modes, errors are greater than 80%. The prognostic equation for a single mode coefficient is examined. Results suggest that, for medium depth, large horizontal scale tropical modes, a significant error source is the balance condition itself. For these modes, the time scales of their diabatic forcing, observed behavior, and natural (linear) behavior are all similar. In this case, the tendency term in the equations is not negligible.