VERTICAL MODES AND ENERGETICS OF GRAVITATIONAL AND ROTATIONAL MODES IN A MULTILEVEL GLOBAL SPECTRAL MODEL (INITIALIZATION, BALANCED ENERGY, TRANSIENT, NUMERICAL WEATHER PREDICTION, NORMAL)

The energetics analysis is made based on the NCAR Community Climate Model. As usual, the normal modes of the model are computed through the method of separation of variables. One difficulty, which is studied here for the first time, is that the discrete vertical structure equation is not unique. For some typical vertical profiles of temperature and pressure, the solutions of the discrete differential and integral vertical equations are compared. The difference between these solutions is smaller for lower baroclinic modes but larger for higher modes. Moreover, the eigenfrequencies of the gravity waves, and thus their energy, will be affected by the choice of different vertical equation.;New concepts of the balanced energy (BE), transient energy (TE), and balanced gravitational energy (BGE) are introduced. Eastward gravity waves contribute more energy to BGE and TE than westward ones. We notice that the lower vertical modes are responsible for the amplitude difference between BGE and TE, but that in the higher baroclinic modes, both forms of energy oscillate at the same rate. Because the high-frequency gravity waves associated with vertical modes 0-2 contribute little to both TE and BGE, they can be freely adjusted in the initialization in order to suppress the high-frequency oscillations in the forecast.;Longer zonal waves contribute more energy to BGE because of lower frequencies. We note that the balanced energy for each vertical mode remains almost constant in time but oscillates dramatically for each zonal wave. This suggests that it is more appropriate to express the energy in terms of vertical modes rather than zonal wave numbers in order to examine whether the energy is balanced or not during the initialization.;Available potential energy and divergent and nondivergent kinetic energy are investigated both globally and in the tropics. Gravity waves play a more important role in the tropics than globally. To retain the strength of tropical circulations in the forecast, we recommend that the gravity waves corresponding to the internal modes 3-5 and zonal wave numbers 1-6 with frequency lower than 1.07 x 10('-4) sec('-1) (or period longer than 16 hr) not be adjusted by the initialization.