Simulated recovery of the mesoscale energy spectrum from smooth initial conditions

Recently Koshyk et al. (1999) and Koshyk and Hamilton (2001) presented analysis of a control simulation with a very high resolution (~30 km grid spacing) global atmospheric general circulation model. They showed that the model simulated a rather realistic spatial kinetic energy spectrum, notably including a transition from a steep (roughly -3) power law dependence on horizontal wavenumber at large scales to a shallower (roughly -5/3) power law regime in the mesoscale (wavelengths less than about 500 km). A detailed diagnosis of the terms in the spectral kinetic budget showed that the mesoscale kinetic energy was maintained against the parameterized dissipation by roughly equal contributions from downscale nonlinear triad cascades and from conversions from available potential energy (which are local in wavenumber space). Koshyk and Hamilton (2001) speculated that the available potential energy at high wavenumber may be produced by the action of the moist convection parameterization, but it could also result from nonlinear advective cascades as well.

In order to examine these issues from another perspective, a set of two new experiments has been conducted with the model. In each case the model has been initialized with an initial condition smoothed by "Digital Filter Initialization", basically taking a weighted time-mean from a segment of the control run. The kinetic energy spectrum at high wavenumbers is strongly suppressed by this initialization procedure. The model was run for 48 hours and the mesoscale kinetic energy spectrum was found to recover towards the control run spectrum with a timescale of about 10 hours - consistent with the earlier analysis of the statistical equilibrium state. A second 48-hour run was conducted from the filtered initial condition, but with the effects of moist convection eliminated. This also showed a recovery of the mesoscale kinetic energy, but at a significantly reduced rate, showing that the convection does play a significant role in forcing the mesoscale kinetic energy regime. Even without the convection, however, the model seems to produce a mesoscale spectrum that is clearly distinct from the steeper spectrum at larger scales.

References

Koshyk, J.N., K. Hamilton and J.D. Mahlman, 1999: Simulation of the mesoscale spectral regime in the GFDL SKYHI GCM. Goephys. Res. lett., 26, 843-846.

Koshyk, J.N. and K. Hamilton, 2001: The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere-stratosphere-mesosphere GCM. J. Atmos. Sci., to appear in Feb. 15, 2001 issue.