Net thermal effect of dissipating gravity waves and its parameterization

Jim Holton has made fundamental contributions to the theory of wave/mean-flow interactions, including his work on gravity waves and their effects on the global-scale circulation. He has developed important refinements of the celebrated Lindzen parameterization of momentum deposition by breaking waves and first tested it with his two-dimensional numerical model of the middle atmosphere. In the meantime, the importance of the vertical heat transport by dissipating waves has been demonstrated by other authors in addition to the momentum deposition commonly described in gravity-wave schemes.

This work has been initiated by the need to incorporate the heat transfer into the widely used Doppler-spread parameterization (DSP) by C. O. Hines. It turns out that the exact description of the effect, otherwise known as “dynamical cooling,” depends on partitioning of the total wave energy deposition rate between the thermal and mechanical dissipation channels. Since the DSP does not distinguish between the two types of dissipation, certain assumptions have to be made. The resulting expression relating the heat flux with the wave energy deposition rate is then in general agreement with other studies using particular assumptions and may be implemented within any suitable parameterization. More generally, it is observed that the wave dissipation results in an increase of both the energy and entropy of the background stratification as is appropriate for a dissipative process. Since on balance energy is deposited into the mean stratification, the familiar term “dynamical cooling” may be somewhat misleading. The general relation may also be recommended for estimates of the net heating from available observations of wave heat fluxes.